Per the official release, the Rams will add the 215th overall pick, 40th in the 6th round, of the 2015 NFL Draft to their current draft holdings.
The moves that the league alluded to in defining the Rams pick were the losses of Kellen Clemens, Shelley Smith, Darian Stewart and Chris Williams as well as the additions of Kenny Britt, Alex Carrington and Shaun Hill.
Again per the release:
Under the rules for compensatory draft selections, a team losing more or better compensatory free agents than it acquires in the previous year is eligible to receive compensatory draft picks.
The number of picks a team receives equals the net loss of compensatory free agents up to a maximum of four. The 32 compensatory choices announced today will supplement the 224 choices in the seven rounds of the 2015 NFL Draft held
Compensatory free agents are determined by a formula based on salary, playing time and postseason honors. The formula was developed by the NFL Management Council. Not every free agent lost or signed by a club is covered by this formula.
In the end, the Rams are now up to a half dozen picks in the 2015 NFL Draft to supplement a trade that has the organization headed in a completely new direction on the field to say nothing of it off of it.