You can get a list of available missions on any planet or space station by clicking on the Mission BBS button to access the mission computer. Click on any of the missions to get a description of it, or click on Accept Mission to choose that mission. Note: the mission BBS automatically scans your ship registry when you key in your access code and tailors the list of missions to fit your ship.
In Nova, opportunity knocks on any door - you can be offered missions in any dialog, from Shipyards to Outfitters.
Some missions only become available after completing other missions first, or after obtaining a specified combat rating, or government status.