Pause and go to the Online menu, then select Join Job and pick a type. You may not get one you like, but you should almost always be placed with at least a few people. I play on PS3 and really like to do racing, and sometimes I'm lucky and get a group of around 4-6 people that stick around for over a hour doing different races. It's a lot more fun than racing just 1 other guy that starts as soon as any other person joins.
However, there are also many times when I hit Join Job and whatever I pick ends up placing me alone in a lobby, in which case I also have your issue where the invited people never join. I think the main issue is that the game will only invite up to 15 other people, and if none of those people accept or reject, it will never invite anyone else unless you back out and start all over again, in which case it'll invite mostly the same people if you don't switch lobbies first.
If a lot of the join *mission type* options are grayed out, I think you need to be carrying at least $200-500 on your character.
XBL: Stycken Nuggets
PSN: Styck