Taking an archery hunting course is huge. If there is a local archery club, that could get you into contact with other hunters as well. They will be a wealth of knowledge. If you're using recurves, then that's pretty good groups. If using a compound with release and sites, then keep practicing (well...always practice anyway!, lol). Like Superhunt said, you'll know when you're getting pretty good when you don't dare shoot more than one or two arrows at the same spot for risk of ruining arrows.

Most people worry about their spot shooting (learning to judge distance is huge too, or having a range finder so you can scan several spots around your stand ahead of time), finding where to hunt and how to hunt it...and then aren't prepared if they take one. Make sure you have all the necessary items to field dress, carry/haul it out, skin (easier if you hang them), and a walk-in cooler to get it to as soon as possible.

Never ever "force" a shot with archery gear...this is one of the main causes of a bad hit and losing an animal. It's exciting to get them close and you'll be really excited to take your first critter with a bow, but stick to a very strict regiment of having everything ideal before shooting. Animal is unaware of you, broad side or quartering away slightly, etc., and be aware that whitetail react so fast that they will drop their whole body down between your bow going off and the arrow arriving (jumping the string). I've heard many people claim that the deer "ducked their arrow", but it is just them gathering themselves to run away when they hear the noise. Depending on the distance I hold lower than my intended target and let them "drop" into the arrow. Watch some videos in slow motion, you'll see what I mean.

Also if you're ever unsure of the hit, give them a minimum of six hours...I prefer eight. If you jump them up from where they bedded your chances of recovery go waaaay down.