Followers are generally given a set of skills that will improve, regardless of what you equip them with. These will improve with level, but nothing else will. Faendal is always going to do better with bows than with a greatsword, for example.
To this end, the official strategy guide states:
- Sven's skills are alchemy, enchanting, smithing, and archery
- Lydia's skills are in one-handed, heavy armor, archery, and block; not sneak
It's not clear where the rumor that Lydia would make an excellent thief started: UESP mentions she has the sneak skill on the list of followers (I suspect that's where Wikia pulled the information), but her wiki page clearly marks her as a warrior (the correct designation). Nothing about her says "stealthy": she starts with a sword and board and tells you over and over that she's there to protect you.
While the official strategy guide does list what each follower's skill is, with the exception of Lydia, UESP's version matches up with the strategy guide, so it should be pretty accurate to determine what skills your follower has.
But if you wanted to do it without consulting a guide or a wiki, it's generally common sense and usually based on what equipment they come with. Lydia comes with a sword and shield, so her skills are one-handed and block; Faedrun comes with a bow, so one of his skills is archery; and so on.
In general, if I pass an obstacle that my follower can't navigate, I can walk up ahead a bit then rest for an hour. This almost always forces your follower to teleport beside you.
Best Answer
Spells
You need the Healing Hands spell. Or Heal other, or Grand Healing. Note that these spells only work on living followers, not undead or robots. If you have dawnguard, Heal Undead heals undead.
Protected Aka "I'm invincible"
But you should not worry, most non-quest followers are immune to death by normal enemies. They are protected, if they get damaged enough to die, they crouch, and enemies stop attacking them. They can only die if hit by a random attack that was actually directed at somebody else, an area of effect spell, or if you the player hit them. They can and will die if poisoned.
Potions
You can also give followers healing potions. They will use them to heal themselves. A bit expensive solution perhaps, but it works. Of course, this might be buggy, and they might only use store bought potions. And do not give them fortify health potions. They will die if the combat is still going on when the potion duration runs out.
Difficulty
Changing the difficulty might help. Followers might be affected by the difficulty of the game and might take and do full damage. (not 100% sure of this one, but it used to be true for oblivion at least). But if the difficulty does work, then at higher difficulty they would both do more and receive less damage.
Skyrim helps those who help themselves
Look at the list of followers, and select one who has access to restoration magic. These can heal themselves. Talvas Fathryon from the dragonborn DLC is one of those followers. Or if you have 500 spare septims, get Marcurio in riften. But as followers are a bit suicidal at times, they are not likely to heal themselves when you want them to. Such is life, let them go to Sovngarde if they are eager to go.
They will not heal you. They hate you that way. You should have let them have that sweetroll.
Your droids, they are not welcome
It seems that the Steadfast Dwarven Sphere and the Steadfast Dwarven Spider you can get in dragonborn cannot be healed. I assume they heal outside of battle.