I've seen a bunch of questions about waivers, and although I definitely do not think of myself as an expert, I did read an article about them by Steve Phillips over on ESPN.com

Usually, I think the guy is an idiot (heck, look at what he did to the Mets), but this was actually a pretty informative article

http://insider.espn.go.com/mlb/columns/story?columnist=phillips_steve&id=2130379

Alas, it is insider only, but here are the relevant bits:

Players can change teams one of three ways on waivers:

1. A player is claimed on waivers and the team awarded the claim makes a trade with the other club.
   
2. A player is claimed on waivers and the player's team just decides to dump the claimed player on the claiming team.
   
3. A player clears waivers, meaning that no team claimed him during the 47-hour period, and is later traded to an interested party.

The interesting thing is that most teams try to get all of their players through waivers -- not because they want to trade them, but instead to protect themselves just in case they get an incredible offer for a player.

Once a player goes on waivers any team can put in a claim, but the claims are awarded in order of

1. League -- American League teams have dibs on AL players before the National League gets 'em and visa-versa
   
2. Record -- When comparing two claims within the same league, the team with the worst record gets dibs.

Usually, when a player is claimed, the owning team pulls him back - they didn't really want to trade the guy and were trying to sneak him through. However, if nobody claims the player within the 47 hour waiver period, the player has "cleared waivers" and can be traded to anyone.

Gammons had an article about the guys who have cleared waivers. Among the hitters that cleared were: Piazza, Griffey, Sweeney, Frank Catalanotto, Dustan Mohr, Todd Hollandsworth, Todd Walker and Edgardo Alfonzo.  Sadly, one of our favorites, Adam Dunn did not clear - so we realistically have no shot at him. For those of you with insider, here's the Gammons article:

http://insider.espn.go.com/mlb/gammons/story?id=2135848

One other interesting thing to note - if a team wants to trade anyone on the 40 man roster, that player must clear waivers. So, for some of our AAA guys to be included in a waiver trade, they too would have to clear waivers. (Not bloody likely in the case of someone like Juan Cruz).