Hi R.,
My eight month old is doing the same thing. We use the Avent sippy cups, and I started giving him them at four months when I started giving him solid foods.
He started out just looking at it, then started drinking from it when I gave it to him, then starting picking it up and chewing on it, and now will drink by himself when he's not throwing it on the floor.
It's not a constant thing for him either. Sometimes he'll drink out of it great for lunch and by dinner he has no idea what to do with it again. :) They're too little at this point to be consistent I've decided. :)
Don't worry, and don't be afraid to try a couple different kinds to find what works best. I have the Nuby $1.97 specials from Wal Mart too and he likes those as well. They just seem to spill more than the Avent ones I've found and I'm trying to keep the messes down as much as possible.
Also I know Avent has a handle set that's a trainer for their bottles, I don't know if you're breastfeeding or using formula, but it might be helpful to use something like that. I'm not sure if other brands have that or not. I just started using that with my son, and in the four days I've been using it he's gotten a lot more coordinated with holding things himself.
Good Luck! :)