I'm not an expert by any means, but I've been bowhunting since my youth. I prefer firearms, but like the challenge of the bow, and it's a great way to extend your hunting season. Here's a few tips that could be useful to anyone, but are geared more toward the beginner:
1. Bows are a lot like pistols, in that personal preference makes a huge difference in selection. If at all possible, shoot several at a pro shop before settling on a brand or model.
2. It's not a he-man contest, so you don't need an 80# draw weight to hunt. I prefer 60# for midwest whitetail hunting (where my shots average 15-25 yards), and 70# for southwest hunting where the land is more open, and longer shots are usually necessary.
3. You don't need the latest and greatest, but technology certainly does have its benefits. MANY deer were taking with longbows, recurves, etc., so yes, they'll still work. However, a modern/efficient bow may have a lot of little perks that will benefit you (higher KE with lower draw weight, higher let-off %, speed, forgiveness, etc)
4. When practicing, make sure you use good form (have a pro show you; not a buddy). 5 perfectly-placed target shots are more valuable than 20 sloppy ones. You're going to use muscles that likely haven't been used before, so you're going to get tired quickly. QUIT PRACTICING when you get tired. If not, you'll only develop bad habits.
5. Don't get caught up in the "speed trap" with bows. Many people judge a bow's value and effectiveness by how fast it shoots. Sure, it'll allow you to make longer / quicker shots since it will shoot a bit flatter, but if you're not comfortable with the bow or have good form, you'll only miss quicker.
6. Even though there's not much to clean on a bow (other than wiping the dust off it), maintenance is still important. Make a habit of thoroughly inspecting the string & cables every time you shoot. Rub them down often with bowstring wax. If it's starting to fray, get it replaced. Lots of people recommend replacing strings every year regardless of how much it's used. Personally, I replace mine about every three years (don't forget that new strings stretch with use, and will require a break-in period).
7. Practice from multiple positions (sitting, kneeling, standing and elevated). If shooting from a raised platform (treestand), make sure and bend at the waist instead of just lowering your bow arm.
8. Just like firearms training, occasionally practice while wearing all the gear you'll likely be wearing while using the bow. You don't want to find out at the wrong moment that you're hunting jacket is so bulky that it makes contact with your string when shooting.
9. Practice at unknown distances; not just 10, 15, 20, 30, etc. This will make you better at range estimation (which is much more critical with stick and string). I like using a target that I can throw & roll around on the ground to get unknown distances.
10. Have fun!
And if there's nowhere to put a treestand on your property (if you're like me and live in the city), shoot from the rooftops if your neighbors won't freak out...:-D I even have my spotter calling my shots for me: