I am 15, 5 foot 8 and 110 lbs. I have never ridden before.What size dirt bike should I get?

well for that hight and weight i would pick a 125 if you just want to put around if you want to race i would go with a 230 for ya

You don't say what use you want to put the bike to or if you intend to race it. But at 5'8 anything like a 85cc, ttr125, klx125 are all going to be a bit small, although you are quite light for your height so may find anything too much bigger hard to throw around.
The best thing you can do is go to a dealer and sit on a few and see if something like a crf250f would be okay. You would have no trouble with it with how tall you are but you need to see if you are able to deal with the weight of it.
You should be okay with the weight though as my son is lighter than you and can pick his 250cc up.

Well in my opinion for your hight I would go with a F 250 (Honda, Suzuki, Yamaha, or Kawasaki) that would be pretty good if u wanna ride on a motocross track. Weight wise you are a little too light for it but I think you'll do fine on it. An 85 is way too small for ya. I'm 17 and 5ft 7 160 pounds and i ride a CRF 250. Hope it helps :P

a 125cc 2 stroke may be to much power for you. Look for a Honda XR 100, CRF 100, Yamaha TTR 125, Suzuki DRZ 125 or a kawasaki KLX 110. good begginner bikes that aren't super big and are all 4 strokes. Look for KX 85, CR 85 or RM 85. 2stroke small race dirtbikes.