The ability to re-enter a tournament is limited at this time.
Any tournament type where re-entry is available to players, would have a "Re-Enter" button available on the tournament standings screen/page. If the "Re-Enter" option isn't offered on the tournament standings screen/page, then re-entry is not an available option for that specific tournament.
The ability to re-enter more tournament types in more game titles will continue to be rolled out in the near future.