If your actions and dialogue hit items on his likes list, then his affection for you will rise; conversely, if you keep triggering his dislikes, he's going to start to loathe you. You'll gain your five main companions through your class' storyline, with your first companion assuming a combat role that Bio Ware deemed most important for you to have as soon as possible.
If you don't care about these, then you can safely ignore the affection system, otherwise you're going to want to get on your companions' good sides over the course of the game. From my long experience with Bio Ware, I suggest you keep in mind that initial impressions and assumptions about one's companions may turn out to totally not be the case, as the studio is infamous for writing dark secrets, mysterious motivations, and quirky personalities that come out over time. Your starship, when acquired, will come with a droid (either 2V-R8 for Empire players or C2-N2 for Republic players), which can be used as a companion with one large caveat: The droid cannot fight.
This is tricky because none of your companions will share the same set of likes and dislikes, which means your actions -- if consistent -- will end up ticking some of them off. It can, however, heal and assist with crafting, so there's that.
(HK looking at you)Do these fixes include letting Akghal Usar get crits on crafting and materials missions?
I spent several hours one day running tier 6 mats missions, and I gave that ugly mother a boatload of the rich/bountiful missions, and he never, ever scored a critical success as a rank 50 companion.
You'll also want to be on the lookout for companion-specific gear in the game world and through quests. When it comes to group content, think of companions like a bandage: They may not be ideal solutions, but they'll hold a group together adequately if needed.