Some missions will be offered to you directly but many can be found in, or become added to, the Mission Bulletin Board System (BBS).
The "Campaign" (AKA "main plot") is only available through the Campaign game start. All other missions are available in every game start. NOTE: if playing the Campaign, some side plots (and DLC systems) cannot be accessed until the first gate (to DV) has been used, or after the Campaign completes.
Links to info about the different types of missions:
The first four links contain spoilers. The Tutorials are located in the BBS.