We need to clarify whether we are talking about a tie
in a tournament game or a tie
in the tournament standings.
Ties in a tournament game
If the boardgame has its own tiebreaker (for example, in Wingspan the tiebreaker is "number of food tokens at end of game"), that tiebreaker is applied, and then the tournament standings do not record it as a tie. If the boardgame itself designates a tie, or if one player is expelled for being out-of-time resulting in the other players being deemed to tie, then the following rules apply:
Round robin: Each of the tied players receives 0.5 tournament points. Demonstration:
https://boardgamearena.com/tournament?id=521696
Swiss: The tournament points are divided among the tied players. For example, suppose it's a 4p game where the attribution of tournament points for each game is "..., +6, +4, +2, 0". Then in a two-way tie for second-third each of the tied players gets +3; in a two-way tie for third-fourth each of the tied players gets +1; in a three-way tie for second-third-fourth each of the tied players gets +2; in a three-way tie for first-second-third each of the tied players gets +4. Demonstration:
https://boardgamearena.com/tournament?id=410841
Multiplayer elimination: If one or more (but not all) of the tied players can advance, then the lowest player-id number(s) will determine who advances. (The "seniority rule" or "oldest account advances".)
Single elimination: Who advances is presumed to be a coinflip (random equal-probability selection between the two tied players). See
https://boardgamearena.com/forum/viewtopic.php?t=41794
Ties in the tournament standings
When viewing the tournament standings, click the greater-than symbol (">") to the right of the word "Players" above the standings. That should expand the standings letting you see some of the "tiebreakers".
Round robin: In general, two players tied on tournament points will be ranked according to "score difference"; i.e. the total of their margins of victories in games they won minus the total of their margins of defeat in games they lost. [What I'm not certain about is whether "number of wins" is also a tiebreaker. For example, suppose there are 15 players in the tournament and I have 7 wins, 4 draws, 3 losses (9 tournament points) while you have 9 wins, 0 draws, 5 losses (also 9 tournament points). Do you outrank me because you have more wins and if so, is that applied before or after the "score difference" tiebreaker?] If the number of wins, draws, losses, and score difference is the same, then rank in the standings is determined by player-id number (i.e. older account prevails). See
https://boardgamearena.com/forum/viewtopic.php?t=34998
Swiss: In case of a tie in tournament points, the first tiebreaker is tournament points of all the opponents that each player faced. Next tiebreaker is "opponents' average Elo" (which does not relate to the present system of Elo but the system which BGA used years ago). [If there is still a tie in the standings after applying both those tiebreakers, then I don't know what happens.] See
viewtopic.php?p=178086#p178086 and
viewtopic.php?t=18243&start=90#p138745