They might have followed you home, or been foisted on you by someone, but however you got them, if you plan to keep your Follower, you have to think about them, and treat them right. Remember a Follower is not just for Christmas! Also, they’re useful pack-mules.
Mostly I’ve been wandering around with Lydia, and I’m told that other Followers may have slightly different behaviours. I’m pretty sure that the following will apply to most Followers though.
Firstly, remember that most Followers are not immortal. They can die. I’ve read a few places that once an enemy has removed all your Follower’s health, they’ll concentrate on you and leave your Follower alone I’ve seen a lot of evidence that this isn’t true – especially as I have a ‘sneak’ character. A final blow, whether from an enemy, or you – and given that Lydia just loves to step into the way of arrows, or sword blows, this is likely.
Once your companion is dead, they’re dead. You either have to live with that, or reload from a previous save. You’ll have to ask your conscience which way to go here.
Of course, the best way to go is not let them get killed in the first place. This can be rather tricky, especially if they’re brave (i.e. stupid) and wander into fights with no regard for personal safety. Lydia often tells you that she’ll guard you with her life. The problem with that is she can only do it once.
A lot of this becomes somewhat worse when you have a sneak character (as I mentioned I do), as often your Follower will catch the attention of enemies long before you do, and often wade into battle before you’re ready. So I often find that the best thing to do is just keep them out of battles entirely.
In dungeons, I usually ask Lydia to stay put while I scout on ahead. Usually I’ll wipe out whatever is there, then come back, drag her along for a bit, load her up with loot, then repeat the process. I very rarely let her engage in boss-fights.
With dragons (with some being a little unexpected), my tactics are to make myself visible (usually after getting off a couple of sneak attacks, if possible), so that the dragon now has two foes. In most cases I’ve found that Lydia is incapacitated, but not killed in such circumstances. Most cases.
If I lose her more than once (i.e. I have to reload to get her back, and have to do it again), I usually make her stay put somewhere while I take on the dragon myself. This is usually only possible in places where you know dragons are going to be. It doesn’t always work for the “random encounter” ones. It also depends how far back your last save was …
You can help keep them alive by giving them weapons and armour. While they’ll happily carry anything for you, they will use things that attract their attention. Note that this isn’t always the best stuff, but as long as it’s better than what they started with, it’s a good start.
Lydia often surprises me by conjuring up a wolf or similar during battles, or using fire or frost spells with the staffs I make her carry.
Another downside to Followers is that they’re often clumsy. You may have taken great pains to notice and avoid traps and pressure plates, then your Follower will just stumble over them and either get hit, or the trap will catch you. If they get hit, then after you’ve finished laughing, you may have to reload, or simply try to work out how best to get them to follow you to avoid doing it again. In some cases it’s best to get them to stay in one place while you do the work. In a large place, especially one that means you don’t retrace your steps, this can be troublesome, though. In a few cases I’ve led my Follower back outside, told them to stay, then used fast-travel to pick them up when I’m done. This did mean I lost my pack-mule for that dungeon though …
Also, Followers aren’t very good at finding their way around the landscape. They often get lost. Don’t worry too much about it. They’ll eventually catch up. Fast travelling to a place, or going through a door into a building interior often helps.
In the end, you have to decide if a Follower is worth it, and perhaps try various ones to find one that suits your style. Lydia doesn’t suit mine, but I like her too much to give her up just yet. If you do decide to keep one, however, you should look after them, and remember they need a lot of hand-holding to be truly useful.