Do what TwoFatNuts said. I play with Kass a lot, and the main problem I have with him is not not getting kills,(627, 288,494 k,d,a with him, and a lot of that is from when I first started, he was free, and I played crappily with him) it's that in team fights, he isn't the greatest.
I rush Mejai's first, then sorcerers shoes, then Zhonya's. After that it depends on the game. Often I'll get guardian angel next, though sometimes I get archangels or deathfire.
Guardian angel really is a good item for Kass, first, it helps keep your Mejais full, second, with many champs, it will save you for a second, only to have the whole team kill you in 1 second after you spawn again, with Kass, I have escaped 5-on-1 ganks with it because of his riftwalk. By the time I get mejai,sorc,Zhon's, I usually have enough AP to destroy most people anyways.
As far as getting kills, again, do as FatNuts says. Don't take on a full HP champ (usually), during laning, harass with null-sphere, untill they are about half-3/4 health, then rift in, nuke, get kill. (unless your laning against a healer, then just use null to get last hits) In team fights, wait in the back, maybe throwing a few null sphere (especially on casters, you own Ryze's and Karthus's) then when someone is low, rift in, nuke, and get kills, then rift out.