This explains the procedure pretty well: https://en.wikipedia.org/wiki/Designated_for_assignment
A few comments:
1) Latos does have more than 5 years service time, so he can't be sent to the minors without his consent.
2) He would have to clear waivers for the Red Sox to pick him up as a free agent. I doubt he would clear waivers; some team lower in the standings would almost certainly take a shot at him as it would only cost them around $300K (prorated portion of the MLB minimum salary).
3) More than likely, if they want him, the Red Sox would have to trade for him in the next week, which would cost players; I'm pretty sure that draft picks cannot be traded by major league baseball teams.