The NHL free agency period will open on July 5 and 12PM and Pierre LeBrun notes that teams will be able to talk with free agents from other teams starting on July 3rd and 4th.
Players can not sign with new teams until after the signing period opens on 7/5 at 12PM ET.
In the CBA, the critical dates calendar notes that that starting next season, a regular league year, players who will be unrestricted free agents can start talking with teams the day after the NHL draft but can not officially sign a contract until the UFA period begins on July 1 at 12PM.
RFAs can start talking with teams on the Tuesday after the NHL draft but can not sign until July 1 at 12PM.
Also of note is that the deadline for teams to send out qualifying offers to retain the rights for RFAs is July 2.
The buyout period ends at 5PM on July 4. It opens tonight at 11PM.