Sizing an electric RC brushless motor
I am going to try to keep this as simple as possible and present you with just the needed information. some of this information you may already know and may wish to skip sections with "BASICS"

An RC brushless motor has 3 wires. The voltage to these wires are PULSED in a particular pattern that requires a microcontrolled Electronics Speed Controller (ESC).  The ESC takes the power from your flightpack and controls these voltages by the input comming from the servo wire that goes to your Rx.  The ESC May or May not have a built in Battery Eliminator Circuit.  If not, you need to supply the Rx with power through a seperate battery or seperate BEC. Often smaller ESCs will have a Linear Regulator BEC which is inexpensive but can heat up (research this seperatly). External BECs are often a "switcher" type which heat up less.

Brushless motors do not have brushes or commutators. They have wires and magnets.  The wires are energized through the power from the ESC and thus create an electromagnetic field that opposes and attracts the magnets on the motor.  One of the more commonly used motor types used (which I focus on) is the outrunner.  The outrunner has the windings on the inside and the magnets on the outside. The outside spins while the inside is stationary.  The Inner core is connected to one end of the motor where the wires attach and where the motor mount connects to.  the outter core is often called the "bell". Because if you pull the motor apart, the outter part looks like a can with an open top (BELL).

You can mount an out runner from One side only. The side where the wires are. The main part of the motor (BELL) will spin.  But there are 2 directions you can face the motor from the mounting point.
1) If you have a prop adaptor that mounts to the BELL side, then you often use an X mount and mount the otherside to a firewall.
2) If you have a prop adaptor that mounts to the stationary side, then you have to have a long shaft on the stationary side and poke it through a firewall (or special motor mount) and then attach the prop adaptor from the front.

When sizing your ESC, you need to think about a few things.
1) Physical size (will it fit where you want to put it?).
2) Max continuous current (will it handle the amount of current you will put through it?), To figure out max current, you first need to size your prop and calculate the current draw.  It is best to over rate your ESC to deal with situations where your current draw exceeds calculations (bent shaft, out of balance prop, ground strikes etc).
3) Max LiPo Cell count (if you want to put a 4S lipo to it, it had better support up to 4S Lipos)
4) Does it have a built in BEC (see ESC Basics) or will you want to supply external power. Many people agree that anything over 3lbs of aircraft or over 4S flightpack require a seperate switching BEC or Rx battery.
5) Airflow, If you don't have good airflow across the heatsink, you may want to over rate the ESC to compensate.
6) Look to get an ESC that is 20-30% more than the max continous current you will run.

LIPO Battery info Basics
Click here for some LiPo info

OK, we finally get to the good stuff. What you have been wanting to know. The first thing you need to know is the approximate weight of your aircraft and how you want to fly it.  This will help determine the target Wattage you will want.  Here is a general table of Size vs. Wattage that many people go by.

Sport/Training : 75-125 Watts per lb
Aerobatic/Warbird flying : 125-150 Watts per lb
Extreme 3D flying : 150-200 Watts per lb

These numbers are very generic and can be massaged with your prop selection.  For example, go a larger diameter prop and get more low end thrust and vertical climb. Go with a higher pitch prop and lower diameter and get more top end speed.  You can make a plane go fast on low diameter and high pitch on 100W/lb , but it won't climb vertically as well as a higher diameter/low pitch prop using the same wattage.  What is high diameter or high pitch?
I tend to give the breaking point at a 2x ratio. If the diameter is greater than 2x the pitch, then it begins the high diameter range (12x6). When the Pitch is passing 75% of the diameter (12x9) then you are getting into a high pitch prop.  I have a few light Foamies/funflies that run on an 11x3.8 slow fly prop and they climb forever on little wattage, but it does not go fast at all horizontally and comes down in a steep dive almost at the same speed it goes horizontally.  When you get to the prop calculator below, look at how changing diameter vs. Pitch affects static thrust and max level flight speed. Increase Pitch one degree and decrease diameter and see how the static thrust and max level flight speed changes.

OK, so you have an approximate Wattage you want to look at.  The next part is to get familiar with a Motor Calculator program. I like to use one of thse calculators. There are others (including ones you can buy) but these are free and gets me close enough.
For my favorate Airplane motors (Monster Power and Tacon Big Foot) from HobbyPartz. I pick out a motor that needs the wattage requirements I have estimated. 

1) Start with the 
ADAMONE calc and set the ESC to custom and a very large Current rating. Otherwise the warnings get annoying.
2) Set the battery to Custom and select your first guess at cell count.  We will tweek the battery later.
3) Select a motor that closely matches the motor you have selected.  In this case for example, we'll size a Monster Power 32. Select the E-flite Power 32 motor from the Motor drop down box.  
4) The E-flite Power 32 is close but not the same Kv as the Monster Power 32.  Now Select Custom Motor and the E-Flite 32 numbers stay there, but you can now change some parameters.  Switch the Kv to match the motor you chose (770 in this case).  (Note: true Kv of the motor may differ by up to 10%). You can change some of the other parameters but the difference is not that significant compared to the error of using a calc to begin with.
5) Now select a prop from the drop down list.  APCe prop and APC slow fly are the most common used props. Most electric props will behave like an APC E prop or an APC Slow Fly anyway.  If you don't see the prop you want to use, then select something close, then switch to CUSTOM for the prop selection and change the Prop diameter/Pitch.
Note: One thing to keep in mind on prop selection is to make sure you can BUY the prop you are selecting. There are more props available than what is listed and you may want to inventory props at your local hobby shop or go online to a supplier like Graves RC to see what they have as you are doing your prop selection.

6) As you are tweeking your prop selection, keep some things in mind.  
7) Now, you have some numbers to look at.  In general you want to use purchase an ESC that allows a continuous current that exceeds the continuous current draw that you will run.  Since the calculator is not perfect, you may find that your current draw (and RPM) may be ABOVE what the calculator says on a fresh battery pack. A good rule of thumb is to add 20%-30% more ESC than you need. (calc shows 30A? buy a 40A ESC).  There is only the weight and size pentaly of a larger ESC.  Using a 60A ESC when you only need 30A is not going to harm the motor or give you less power (it might actually give you more power because the bigger ESC will have a smaller resistance, but not much).

TWEEKING the numbers.
Here are some things to look at tweeking.
The Battery affects the motor performance MORE than people think. A LiPo is 3.7V per cell and that is all that matters righ? WRONG.  A LIPO discharges during use and the battery drops from a resting voltage of 4.20V per cell when charged down to a resting voltage of around 3.65V when nearly 90% depleted. (Table of generic resting voltage vs. remaining capacity). The battery voltage in the motor calc should be set to the resting voltage of the LiPo.  Notice how if you set it to 4.0V, everything increases.  As pointed out by the LiPo info Page,  Internal resistance plays a key role in motor output.  The default Internal resistance in the ADAMONE calc is pretty high compared to most of the LiPos that people are using today.  It is hard if not impossible to find Internal resistance values on vendor or MFG websites.  ADAMONE shows some packs and the numbers seem fairly accurate (but there are some tweeks I'll note).  NOTE that the batteries are shown by capacity (mAh) and C rating.  YOU SET the cell count.  Internal resistance is per cell, so as you change cell count, so does the calc respond.  In general, here is what I suggest you do:  Select the closest matching battery capacity in the Hyperion Section.  If your battery is a Zippy Flightmax, Sky Lipo, Turnigy, Blue Lipo or other generic budget brand, then leave it alone.  If it's a Gens ace, Turnigy Nanotech, Thunder Power, Hyperion or Rhino, then set the battery back to custom, and then tweek the Internal resistance value down a littl (say decrease 30%).  You can alter the capacity and then view how that affects flight time in the Prop Results section of ADAMONE at the bottom.

If the motor resistance is published for the motor, you can tweek that. Remember, you have to select a comparable motor first, then set it to custom to chang Kv and Motor resistance.

Static Thrust vs. Approx Max level flight speed.
One could spend all day pondering different props in order to look at different values for Static thrust and level flight speed.  The max level flight speed is not how fast the plane will go.  That will depend on the drag of the plane and how much the motor unloads in the air.  A higher pitch prop will unload MORE than a lower pitch prop as the speed increases and the load on the prop decreases.  The calc does not show this.    Some will tell you it is a 5-10% decrease in current in flight and an increase of about 5% more RPM.
A data loggeer is often needed to determine how much unloading is going on.  It is however safe to say, that unless your airplane is moving backwards,it will unload in the air and get MORE RPM, LESS current/wattage in flight.

Some people believe it is safe to over Prop a motor.  This is where you select a prop/battery that will give MORE Wattage pull and/or current draw than the motor is designed for.  Heck, I've done it myself.  Often motor mfg will show a BURST current draw for a motor. you can take that also as a BURST wattage draw. Say the motor is rated for 50A max and then says 60A burst.  Well, that means it can burst another 20% wattage for a small period of time. (sometimes 10-15 sec).  This can be done during high speed passes or climbing maneuvers. But should be followed by a low/half throttle period of time to cool back down. You will see BURST ratings on ESCs as well.  What does burting really affect? Heat! Heat is the enemy of motors as well as Nitro Engines.  You can get away with more bad behavior when you ventilate (air comming in and having a place to exit) as well as flying in cooler sub 90F weather.  

Final notes
When looking to size a motor, the Wattage of the motor is one of the important things to look at, but achieving the desired wattage is more time than not, an experimenting game.  The variables involved are many and affect the outcome greatly.  Does the actual motor you have match the specified Kv? (often they vary by 10%). What is the Internal resistance of the LiPo? Try changing or doubling the IR of a battery in the motor calc and see how much it changes!  Is the prop one of the ones listed or did you pick one similar? I often pick a few different props and test with a Wattmeter like the P0 or P1 from Hobbypartz which is reasonably priced and can save your plane from damage when properly used during testing should you accidently over prop it. Ramping that throttle up slowly as you check your current and wattag on the meter can save you more than the cost of that wattmeter.