This is a great topic since I'm doing this right now and learning some of these lessons the hard way.
1) Brainstorming/research
-this encompasses considering everything from discipline(modern compound or traditional), purpose(hunting what type of game? styrofoam/target or whitetail or what?), to online opinion gathering and product/company info gathering, and determining your budget. REMEMBER THE ACCESSORIES. If you have to, print out and organize the info so you can keep straight what models have what features you decide are important you. This stage is where a place like HNI can be soooo invaluable to those of us in the market. But beware the brand-snobs and learn to take the "cut-downs" with a grain of salt. Alot of deer have fallen to an arrow flung from a "non-name brand" bow.
2) Proper FITTING
-go get fitted at a pro shop. Write down all the important measurements and info the pro can tell you. Go to as many pro shops as you can and decide which one you're most comfortable with. Also try to go at a not-so-busy time so they can spend the time with you. Beginner beware the online "pro-shop" and big box discount stores. These should be reserved for those who know EXACTLY what they want/need and how they want it.
3) The fun part(or brain wrecking part)

THE TEST DRIVE. Try out as many bows as you can in your price range. Even test the "bad boys". but be careful when trying out the "high end" bows. They may make you want to stretch your budget to far and you wont be able to get quality "peripherals"(sights, rest, release arrows).
4) COMFORT - You want a bow that feels like an extension of your being. ESPECIALLY if you're doing traditional or instintive. I know all bows are going to feel somewhat foreign, but there should be one bow that just feels right. ONLY YOU CAN MAKE THAT DETERMINATION. Dont force it. Let it come to you. When you're comfortable with the bow in your hand, and you can say with resolute satisfaction and pride(without getting hung up on brand or MSRP) that that's YOUR BOW. Then you will be more willing to enjoy it and you will WANT to PRACTICE. Practice is THE key to this sport.
5) AND POSSIBLY MOST IMPORTANTLY -- DO NOT RUSH INTO A PURCHASE It's better to get the right bow for you, than to just get one "that will do". Plan for this process to take some time. Some guys plan on changing their equipment like some people change their underwear. I plan on using mine untill it dies. (or I die, whichever comes first). So I want it to be the right equipment.
Wow! Didn't mean for that to be so long winded. Sorry guys