Get him out of that vase and into a proper tank!!!
I've heard too many horror stories about those vases!
I'm no expert by any means but I know for sure that the vase is a very bad idea, and you should talk to the previous owner about that.
I keep my big guy in a 1G tank with decorations and plenty of room to swim around. I keep seeing even larger tanks floating around on this forum, and I wish I could get all three of my bettas bigger tanks! I'm sure someone more experienced than myself can educate you in that area.
Definitely do your research on betta care asap! I recommend http://www.bettatalk.com
... it's where I learned everything I needed to know about caring for my fish.
I'm sure everyone on this forum, including myself, would be more than happy to help you out and offer some great advice on caring for your new boy!
Welcome, by the way. :)