These are quests that are not associated with any particular faction. Instead, you pick up on these through conversations that you hear between NPCs, conversations that you have with NPCs, items that you pick up somewhere, or whatever.
They follow the same rules as any other quest - find the quest-giver, do whatever it is that needs to be done, and report back to collect your reward.
Most Miscellaneous Quests are simple enough. Some of them can get a little complicated, some can be exploited to your advantage, and some are hardly worth the bother. It just kind of depends on the quest. There are even a handful of them where you can be the bad guy, if you'd like to go that route. There are a few of the quests where most of the quest is finding the quest-giver - you already have the object, but don't know who to give it to.
Aside from their rewards, most Miscellaneous Quests will boost your Fame by a point or two. In and of itself, this isn't any great shakes, but a lot of Fame points add up over time and can really help. Once your Fame is somewhere up in the 80's (I've heard 85 bandied about, but haven't verified it), guards may overlook your petty crimes. And once it's 100+, they might even overlook some of the more serious ones.
Frankly, I'm not sure that's a terribly accurate claim. With a Fame of 130+ and an Infamy of 2 (one point each for joining the Thieves Guild and Dark Brotherhood), I've been busted for very petty stuff like trespassing and was only given the standard options of pay the fine, go to jail or resist arrest. Granted, this was the Imperial City guards, but they should behave like any other city guard.
However, I can accurately claim that you'll find that just about everyone likes you more, which means you'll get more cash for your loot without having to butter up the merchant as much. And you'll be able to get information out of NPCs much more easily (and cheaply). On the downside, that means fewer opportunities for playing the persuasion mini-game, so those of you with Speechcraft as a Major skill might find yourself a little handicapped.