I might be blind but I don't see a dialogue option to open up my companion's skill screen.

UESP tells you what followers are "trained in", though to what extent it doesn't say. I'm also aware that you can edit your companion's level in skills via the console. There's no option to see the stats of your character in the standard game, I think I'm right in saying.

correct. only via console or uesp, as muzzy said.

Open the console, click on NPC. You'll see their ID number displayed in the middle of the screen. Type, for example, "getavinfo twohanded" to see their skill level with two handed weapons. This works for every attribute, here's a list: http://www.uesp.net/wiki/Tes5Mod:Actor_Value_Indices

Of course, if you're not playing on PC, then no, there's no way to see NPC attributes.

at least you know youre not blind...

Thanks, I guess I will just use the console. Seems like a huge oversight that you can't see all of a follower's skills in-game.