I remember on some fallout game, you could ask them what weapons they're better at using. How do I know what my companions are best at in Skyrim? Or they're even on most things so it doesn't matter?

For instance, I gave my companion (solitude's housecarl) a greatsword but I don't know if she's level 15 at 2-handed weapons and 50 at 1-handed and blocking. Is there anyway to know other than trying to guess from how she performs?

The wiki has some info but otherwise not that I know of. I'd like more info too.

The same with armor. I was thinking of making some light armor for her (just because it's sixier) but I have no idea if she turns out to have terrible skill level at that and a good skill level with heavy armor.

If you are on PC you can use the http://elderscrolls.wikia.com/wiki/Console_Commands_(Skyrim) getav or getavinfo (e.g. getav onehanded) to check their skills.
Otherwise as has been said the http://www.uesp.net/wiki/Skyrim:Followers has some information.

However, all housecarls are proficient in heavy armor, one-handed weapons, archery, and block.

http://www.uesp.net/wiki/Skyrim:Followers


Some info on this page may not correct, though. At least it contradicts the game guide. Remains to be seen which one is most accurate, I suppose.

edit: oops Rosean already posted that link....

Thanks, I kept going to the page of the follower I was looking for, not the general followers page. That helps a lot. The console command also works great.

As a side note, you might have heard mention that NPCs, including followers, do not statistically level up or scale as your character does.
This means that if you acquired Lydia at say 5 and then level up to level 50, Lydia would still have the skills and health as if she were level 5.

There is however a way to bypass this on the PC and have the game recalculate your follower's (or any NPC's for that matter) skills;

• Open the console and click your follower, a parenthesised number should appear at the top of the console.
  
• Write 'disable' and press enter, your follower will now disappear. Fear not.
  
• Close down the console and let the game run for a few seconds.
  
• Bring up the console again, make sure that the parenthesised number is still at the top of the console, write 'enable'.

Your follower should now pop up again with recalculated stats equal to his/her level.