The two most common ways I think are "roll a d20 (or possibly some d6's) equal or under your ability score" or "roll d20+ability modifier, meet or beat a target number". The latter I believe is the default for DCC, except for Luck checks which use the former.
I don't really like checking against a DC. Not much logic to it, I just don't like it. Conversely, it does cause a bit of confusion when most everything in the game is roll high except ability checks. (I run for a lot of new players)
What about this instead for basic ability checks?
Assume a red (or whatever) d6 acts as the "target die". You roll it along with a different die based on your ability score and try to meet or beat the number showing on the target die.
There is no real reason to do this. It's just for the sake of variety. You would use it for anything you would normally use a generic ability check for. If you wanted to get fancy, you could also change the target die for tasks of varying difficulty. On the one hand it seems kinda wonky, but I can easily memorize it (d6 for no modifier, and steps up or down from there), and I doubt telling players which die to roll is any more difficult than explaining roll-under for the millionth time.
Thoughts? I think I'll try it out next time and see what the players say...