I'm going to quote from the UESP:
There are many ways to contract the disease, all of them involve encountering hostile vampires and letting them attack you. However, rather than let them hit you in melee, you should keep your distance and only allow them to cast their draining spell as this is the only attack that can impart the disease. To speed up contraction, repeatedly lose and gain sight of the target vampire so the spell is cast multiple times. The check for giving you the disease is passed only when the draining spell hits you, not over sustained action.
So the trick is to fight Vampires and force them to use their Vampiric Drain spell on you. Exploit Line of Sight for maximum casts.
Followers have stats just like the player in skills and health. Those values are static and are set the first time you enter/load the zone that they are in. There are also maximum level caps for followers should your level be higher than that the first time you encounter them.
For example, most people meet Lydia very early on and she'll end up being locked in with 100 health and skills in the 20s, so she won't be as effective as Jordis (the housecarl you get in Solitude) whom you'll usually meet much later on since the house costs 25k gold to purchase.
If you are on the PC, there is a way to force an NPC to level up by resetting them:
- First, remove all the gear from the follower (at least the ones that you want to keep).
- Walk up to them, be as close as possible, open the console with the ~ key
- Click on your follower. When you do so, a string will appear at the top of your console that represents your follower's reference ID.
- On your console, type disable, then follow it up with enable
After this, your companion will be 'reset' to match what your current level is. Their health and skills should be improved.
Finally, keep in mind that all followers fall under a general category: warrior, thief, or mage. Lydia, for example, is a warrior and will never gain a sneak skill above 15 no matter what level you meet her at.
Best Answer
You can try to use this mod to enhance their stealth. You can't really make your companions invisible, but what you could try is using a command in the console to spawn a Shadowcloak of Nocturnal and making them equip it. However I can't find you the specific item code.