Calculating POWER, Battery & ESC Requirements
 
Normally we'd build an airplane and plan the power requirements accordingly. Many of us however end up with a box full of parts and what to know what motor, ESC and battery combination will work for a given flying weight. We'll assume I found the following in my parts box:

Park 370 Outrunner, 1350 Mah 11.1 VOLT Lipo & 15 AMP ESC

First we need to calculate the POWER in WATTS that our motor will produce. We can look to the chart below and see what flying weight we can handle for the level of performance we want. Our Park 370 is rated at 9 AMPS continuous so:

VOLTS x AMPS = WATTS
11.1 x 9 = 99.9

The same motor with a 7.4 VOLT Lipo would only put out 66 WATTS
7.4 x 9 = 66

Now we can see what our target weight is for the type of flying we want to do. For 3D flying I'll want to keep the weight under 12 oz or so.

50-70 watts/pound: Minimum level of power for decent performance
70-90 watts/pound; Trainer and slow flying scale models
90-110 watts/pound: Sport aerobatic and fast flying scale models
110-130 watts/pound: Advanced aerobatic and high-speed models
130-150 watts/pound: Lightly loaded 3D models and ducted fans
150-200+ watts/pound: Unlimited performance 3D models
 
Battery Draw & Capability
 
Your battery must be able to supply the burst AMPS the motor is rated for. A Park 370 is rated for 9 AMPS continuous and bursts slightly higher so:

Continuous AMP draw = (mah * 0.001) * (C continuous rating)
OR:
Continuous AMP draw = (1350 Mah * 0.001) * 20c OR 27 AMPS Continuous

We've got PLENTY of juice for this motor/ESC combo.
 
ESC Speed Controller
 
The ESC must be rated high enough to accomodate the burst amperage of the motor as well. In the Park 370 example we can burst to 12 amps. Since our ESC is rated well above the 12 AMPS we might burst to we are good to go.
 
Summary
 
Using the calculations below you can determine the appropriate motor/ESC and battery for a given flying weight or determine in reverse the flying weight the combination will support.

How much power is my motor making?
VOLTS x AMPS = WATTS

How many AMPS can my battery supply?
Continuous AMPS = (mah * 0.001) * (C continuous rating)