yeah, basking light, deep enough water so that if he gets flipped over he has no trouble getting back the right way (cause if he cant get flipped back over he'll drown) get a stack of slate so you can build a spot he can get out of the water and have the basking light shining on the rock), a decent filter (we use the whisper filters where i work), a calcium block or 2 depending on the size of the tank,
and ALWAYS wash your hands after handling it and if you have kids make sure you make it clear to them to wash their hands after cause turtles are known to carry salmonella
you can feed it a variety of stuff, pellets, fish, frozen foods.. feel it out, other then that its pretty much like keeping a fish tank, change the water once a week and away you go.
my turtle when he was basking would stick all his legs out (like he was trying to fly) it was rather interesting lol
and later down the line if you can swing it get a custom made tank (square not rectangular)
forgot to add from your description it sounds like you have a painted turtle
not really green but they have the white stripe on their head