The most important thing about bra fitting is to achieve a stable, comfortable fit where the band is tight enough to provide support and the cups are large enough to fit your breasts. The band should be straight across your body, not riding up, and the center gore (the part of the bra between the cups) should be sitting flat against your body.
To figure out your band size, measure around your underbust--the place right under where your boobs end. Do it in front of a mirror and make sure that the tape measure is sitting horizontally straight. This measurement will help indicate your band size. If you want a tight fit or have very heavy boobs, you'll want to try a band size that is the same as your measurement in inches (so if you measure 30 inches around, try a 30 band). If you want a slightly looser fit for comfort, without sacrificing stability, add 2 inches to your measurement (so if you measure 30 inches, you'd try a 32 band). Don't be afraid to try multiple band sizes. If your measurement is not an even number, you can either add or subtract one inch to get your size, depending if you'd prefer a tighter or looser band.
Band size is important to figure out, but cup size is MOST important. You can find more detail on that in my post here. Most women will find they are wearing a size that is too small. A great starting point to figure out your cup size is the Sophisticated Pair bra calculator. Another good one is the Curves and Corsets calculator. These two are the only calculators I've found online that are fairly accurate. Based on what these calculators tell you, you'll want to order A TON OF BRAS. Order bras in the suggested cup size, one size smaller, and one and two sizes bigger. (Don't worry, you're going to be returning most of them.) You need to try a lot of different shapes and sizes in order to figure out what works. Bravissimo, Figleaves, Brastop, and Large Cup Lingerie are good places to start looking for bras.
When you try bras on, YOU MUST 'SWOOP AND SCOOP' your tissue to figure out if the size is correct. Basically, reach into the bra cup and pull up all the tissue. You'll find that a bra that might have looked too small will now fit; a bra that might have seemed like it fit will be revealed to be too small. You must swoop and scoop every time you put on a bra to make sure your breast tissue is being supported and lifted, not crushed and damaged.
To increase your success, it's best to also educate yourself on breast SHAPE as well as size. For this, check out my posts on figuring out the shape of your boobs, more detailed information on the same, and figuring out what shape you like to get from a bra. These posts will likely also help you figure out what bras to try.
You can also check out my brand overviews on Freya, Panache/Cleo, Curvy Kate. More overviews to come on Bravissimo, Fantasie, Tutti Rouge.
Beware of any website, store, brand, or size calculator that uses "American bra sizing"! There is no such thing as a standard of sizing in America. Most brands that market to America and reputable stores in America will usually use UK sizes. That is, in proper UK sizing, the cup sizes are AA, A, B, C, D, DD, E, F, FF, G, GG, H, HH, J, JJ, K, KK, L. Each size is one size bigger than the one before it--there is no such thing as "half sizes"; some of the cup sizes are just called by a double letter while others are called by a single letter. One really odd thing I have seen is that certain online retailers only stock the single-letter sizes, as though they believe that the double letters are "half sizes" (they aren't!). Be cautious with retailers like that. If you see anyone listing sizes in a way different than what I've listed above, be careful when ordering from them because what you get may not be what you expect. If you encounter an American bra whose cup size is listed as "DDD", this is the equivalent of a UK size E.