How do I resurrect companions / followers?

There is No "legal" way to Do this.

But you can use the ressurect command in the console on PC. (see here Skyrim Wiki )

Console commands (PC only)

If playing on the PC, use the console commands prid <RefID> and resurrect 1. Your follower should go back to life after entering these commands correctly.

prid targets an entity - your follower in this case. Search for your follower's RefID here: UESP.net Skyrim wiki 'Followers' article

Another method to target instead of using prid <refID> is to open up the console and then click on an entity (like your follower's body), this will automatically do prid <RefID> for the clicked entity. This is useful if the body of your follower is visible and near you.

Teleporting lost or far follower

If your follower is still not near your vicinity or not visible after entering resurrect 1, try teleporting your follower to your location using the moveto player console command (after entering prid <RefID>).

moveto player moves that targeted entity near the vicinity of the player.

Your follower should now be near you after doing this.

If for another weird reason, your follower is still not near your vicinity or not visible after doing this, they may have been 'disabled' from the game (might happen with NPCs that are long dead), making your follower not appear in the game. Type enable in the console to remedy this. If your follower still isn't up, type resurrect 1 again.

Another option is to make your follower immortal as mentioned in an answer by Renan here.

More info on console commands here: http://uesp.net/wiki/Skyrim:Console

There is no way to resurrect lost companions. Any NPC who dies is dead forever.