How do people get invited to Gatsby’s parties?

Generally speaking, you don't need a formal invitation to attend one of Gatsby's legendary parties. Word of mouth spreads like wildfire, and the next thing you know, dozens of pleasure-seeking party animals have descended on Gatsby's opulent West Egg fun palace like a swarm of hedonistic locusts, determined to have themselves a ball. Certain special people like Nick do receive formal invitations, but for the vast majority it's unnecessary. It's pretty much open house chez Gatsby; people just turn up, avail themselves of their host's lavish hospitality, and have a great time.
It's instructive that most people seem not to know who Gatsby is or what he even looks like. Their mysterious host moves unobtrusively amidst the heaving throng of drunken flappers and sundry freeloaders. But they're not there to see him; they're there to be seen. Rocking up at one of Gatsby's shindigs is deemed essential for anyone who's anyone in that neck of the woods.
Although Gatsby's guests are more than happy to help themselves to his food and drink his champagne, they're not so keen on turning up at their host's funeral. This demonstrates their true values—or lack of them—their shallowness and utter vacuity. There's just no social cachet or prestige in paying your last respects to someone you never really knew in the first place.