Derived from Yiddish slang. Originally, 'shtick' means prank in Yiddish.
At Jewish weddings, the guests often do shtick to entertain the bride and groom: either by performing short, funny skits, or by doing awesome acrobatics, or by dancing about with big, showy props like balloons filled with confetti, lace-covered arches, weird hats, etc. and occasionally all three.
Naturally, shtick goes in and out of fashion, as everything tends to do, meaning that if shtick is used at weddings, it always has to be the latest trendy shtick so that it should be cool.
And thus shticky became slang for trendy/cool.