I've played 6 ranked games (3 wins 3 losses) and for some reason I'm still unranked. A guy on my friend's list is ranked with 2 wins and 1 loss. How does this work?

....play 4 more and youll be satisfied.

It can list an ELO before it gets established, ie. before your placement matches are over but it will change a lot.

Even if you are unranked you can still have an elo. If your friend is high enough you will be able to see it.

If you say long on his account it will say "unranked".

10 Games and you can see your elo.

After 10 ranked games will you be able to see your elo in the client.
You can actually see it on the ladder online before you have played those 10 ranked games.

http://competitive.na.leagueoflegends.com/ladders/na/current/rankedsolo5x5?summoner_name=ArthurItis522&=Apply