I played a lot of Tichu during one summer holiday back in high school. I love it, but I have never since found 3 other invested people to teach it to, and teaching newbies and then never playing again is so frustrating that I hardly ever bring it up any more nowadays (similar to Dominion: it was great with the friend I learnt it with, but then teaching to newbies doesn't always get them as invested as we were back then - I must be a bad tutor).
I think we got pretty good at team play (we played with fixed teams, mostly), but I don't think I can offer good advice since I've never played with other experienced players other than that group.
There's the basic: track at least the aces, kings, and specials. Learn to smell bombs (i.e. If you don't see threes, there might be a bomb and so on). About team play, it really depends on the group. Playing with fixed teams is really good because you learn what to expect from your mate. Otoh, it can lead to chronically unbalanced games.