I play very casually, mostly on the Android app. There is also http://aagenielsen.dk/hnefatafl_online.php which seems to have the most "serious" community but I think the UI might be older than the game itself.
There are many different variants around, with different levels of balance. When I started playing I picked a variant and thought I would try to "specialise" in that one, but to be honest there aren't enough players around to do that, so you tend to just play whatever variant you can get a game in.
Generally in a tournament each set of opponents would play each other twice, once as each side. I'm not sure about aagenielsen.dk, but the way it works on the Android app is that if each player wins one game, the ultimate winner is the one who won in fewer turns. I don't think that's a great system but I guess it's the best one there is for elimination-style tournaments.
Most things I've read suggest that the defenders (white) generally have an advantage, but personally I seem to play better as attacker (black). Possibly just a sign that I am a novice!
I got introduced to it at the "World Hnefatafl Championships" that happened to be on when I once visited Sutton Hoo. That sounds grander than it was...
Game is quick to learn but good fun. Gave my brother in law a set this Christmas.
Played a fair amount as a kid. It's fun, but you definitely need to play with folks who don't care too much about losing, as the difficulty for the capturing team is quite a bit higher than the running side. Works best if you can play at least two games, flipping who's playing which side.