Usually, it is the team trading up that initiates the discussion--because there is a particular player they covet. A team that wants to trade down can only make that fact known to the other 31 and then hope someone else has a compatible target.
In general, teams only trade up in the first round for one of five categories of players: QB, OT, pass-rusher (4-3 DE or 3-4 OLB), 3-4 DLs and CB. In the last five drafts--2005 to 2009--there were, as far as I can tell, 25 trade-ups in the first round. Of those 25, 21 were for players in the above categories.
2005: OT Jammal Brown, DT Marcus Spears, CB Fabian Washington, QB Jason Campbell
2006: QB Jay Cutler, DT Haloti Ngata
2007: CB Darrelle Revis, DE Jarvis Moss, QB Brady Quinn, OLB Anthony Spencer, OT Joe Staley
2008: DE Derrick Harvey, OT Brandon Albert, QB Joe Flacco, OT Jeff Otah, OT Sam Baker, CB Mike Jenkins
2009: QB Matt Sanchez, QB Josh Freeman, OT Michael Oher, OLB Clay Matthews
The other four trade-ups were for WR Santonio Holmes, DT Sedrick Ellis, TE Dustin Keller and WR Jeremy Maclin.
So, if we hope to trade down, we need to root for a QB, OT, pass rusher, 3-4 DT or CB falling to 20. If a stellar DT or CB is sitting at 20, chances are we'll take him. The pass-rushing crop looks fairly weak this year, so I'm not sure there's anyone who would inspire someone to move up to 20. The OT class boasts five players expected to go in the top 15 (Okung, Campbell, Baluaga, Williams, Davis) but not much after that. Meanwhile, the only QBs under serious top 20 discussion are Bradford and Clausen.
If Clausen or one of the OTs fall, then we may very well get a call. Otherwise, we'll likely stick to our pick.