The only 3 i know of are;

If a player ranks a pick higher than all other players, then they get that pick.

If two or more players rank a pick equally then it is randomly allocated.

If a player doesn't get allocated a pick their remaining picks are given priority somehow.

I know this because I've never seen a strategic 1v1 where a player gets all 3 of their top picks, but I am interested in exactly how the mechanics work so that i can make the most of them.

All help much appreciated.

Your first two points are actually not correct. You can read about how it works here: http://wiki.warlight.net/index.php/Manual_distribution