Howard Balzer of 101espn.com and the Sports Xchange reports that the "exclusive" signing period for NFL teams could open on Monday, July 25th. The exclusive period would give teams a 72-hour window to begin contract negiotiations with their own free agents, mostly the teams 4-year restricted free agents that were tendered before the lockout. Balzer also reports that teams will be able to sign undrafted free agents and rookies beginning July 25th.
The period before Monday, July 25 would then be used by teams for the purposes of figuring out the new rules, assessing their status under the salary cap, and preparing to unload any veterans with cap numbers higher than their expected contribution justifies.
Presumably, teams will be able to dump veterans and/or renegotiate their contracts as of July 25.
Actual free agency would begin on Thursday, July 28th. That date makes sense, because it's a full week after the sides are expected to completely agree and ratify a new labor deal.