1. You don't get your first companion right off the bat.
There's a lot of information to process when it comes to rolling a new character (and particularly for going into a game for the very first time), so it's understandable that BioWare didn't want to foist companions on you right when you're just figuring out all your skills and what's going on around you.
So don't expect to see your first companion until a bit into your class' prologue storyline. For instance, when I played the Trooper, it wasn't until I was about ready to leave my starter planet that the storyline finally gave me my first minion. Hey, you call them "companions"; I call them "minions" or "cannon fodder."
Pro-tip: If you're having a hard time finding a group to do your starting planet's heroic quests, which require two or more players to do, just wait until you get your first companion, at which point you'll find they're utterly doable.
2. You can tell your companions what skills to use and which to avoid.
Once you gain companions, you'll quickly learn that they have their own AI in combat that may or may not clash with your own fighting style. If your companion is using certain skills that are causing you grief, you can toggle these skills on and off to prevent their automatically being used. It's pretty easy: Expand your companion's skill bar (the little plus + sign) then right-click to turn off automatic usage.
If you want to manually trigger those skills, you can do so from your companion's hotbar, or better yet, your own -- you just need to drag over select skills from his/her/its bar to your own. This might be prudent if you want to tell your companion, say, to taunt a particular target or use a stun at an opportune moment.
3. You can send your companions to do your chores.
Listen up: You're the hero. You don't have to be doing all the dirty work and tedious chores -- that's what companions are for (well, one of the reasons)! One of the coolest things you can tell your companion to do is to take all of your grey items (vendor trash) from your inventory, then run back to town to sell them. It makes the companion unavailable for a short period of time, but it clears up inventory space while netting you some quick credits.
Companions are also invaluable when it comes to the gathering, crafting, and mission systems, otherwise known as "crew skills." Companions in the field can be ordered to harvest a resource, and those back on the ship can be instructed to craft items and head off on potentially beneficial missions. You can even tell your ship-bound companions to do this from afar; it is a high-tech society, after all. They've got cell phones.
It's important to note that each companion has two crew skills bonuses, and these change from companion to companion. You're better off assigning the right companion for the job than to just use any old meatbag for the task.
4. Companions offer unique missions and stories.
If a companion wants to talk to you, you'll see a speech bubble icon pop up over her portrait. At this point, you'll need to return to either a cantina, your ship, or another "private" area to initiate the conversation. Through these conversations, you'll learn more about your companions, work on your relationships with them, and even trigger missions relating to individual companions.
Make sure to rotate through your companions as you adventure -- you can catch up on their storylines on your ship.
5. Companions need coddling.
Each companion has an internal list of likes and dislikes when it comes to his leader -- namely, you. 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.
High affection is important because it unlocks companion-specific quests, allows you to romance the companions (if applicable), and lowers the time it takes them to complete crew skills. 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.
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. This can be offset by finding, purchasing, or going on missions for companion gifts, which can be given for increases in affection.
6. You can woo some of your companions.
Ew! Girls! Ew! Boys! Kissing! Hugging! Hand-holding! "I love yous!" "I knows!"
OK, are we done being immature now? So, yes, some of your companions are "romanceable," which is a longstanding BioWare tradition. Romances aren't possible with all of your companions, and as of right now, they're opposite-gender relationships only. Romances won't come flying at you from the beginning; as in any real-world dating situation, there's going to be some lead-up to the point at which you'll be rubbing noses and making up sickening nicknames for your one-and-only.
If you decide to romance a companion, it's a good idea to pump up her affection to the highest level (see #5 on this list), know the companion's likes and dislikes intimately, and keep looking for opportunities to make googly eyes at one another.
Each class has two romanceable companions -- a female one if you're playing a male character, and a male one if you're playing a female character. There are additional romantic storylines, but only one with your companion. It's up to you to decide whether this is something you want to pursue or it goes against you and your character's motivations.
7. Your class storyline will unlock five companions.
Getting companions is pretty easy; in fact, you'd have to aggressively work to avoid picking them up. You'll gain your five main companions through your class' storyline, with your first companion assuming a combat role that BioWare deemed most important for you to have as soon as possible.
Some of your companions will be of the more exotic Star Wars races, while others will be humans or humanish. From my long experience with BioWare, 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.
8. There are "bonus" companions.
In addition to your five main companions, there are two more that you can pick up (that we know of at this juncture). 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. It can, however, heal and assist with crafting, so there's that.
This next paragraph has a large spoiler, so head down to #9 if you're trying to avoid these.
The final companion you can pick up is a droid designated HK-51 (similar to HK-47 from the Knights of the Old Republic
games). He's a ranged tank/assassin located on Hoth on a crashed ship. Locating him is just the first step in gaining HK-51 as a companion, as you'll have to jump through questing hoops to get him operational (and each faction has its own questline for this).
9. You can customize your companion's appearance.
It's a tad immersion-breaking to see several other players with your exact same companion, even though you know that it's happening. To help maintain the illusion of variety, BioWare has implemented companion appearance kits that will reskin your followers with new colors, hairdos, accessories, and so on.
These kits are gained through a variety of ways. Some are given through quests, some are purchased from vendors, and others are rumored to be available through the special Collector's Edition in-game store.
You'll also want to be on the lookout for companion-specific gear in the game world and through quests. These can give you neat ways to make your companion look the part that he, she or it was born to play!
10. Companions can fill a gap in a group (in a pinch).
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. Companions can be brought in as pinch hitters to fill a role if a group is short a member or loses one. Naturally, they won't be as effective or durable as a human player, but their presence means that a teammate going linkdead or quitting in a huff doesn't necessarily end a run.
There's much, much more concerning companions in the game, but these 10 points should provide you with the foundation to understanding your digital adventuring buddies. Here are a few links that can help you out with more companion specifics:
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