1. Go to the Legends tab
  2. Select the Legend you want to unlock
  3. Unlock the Legend using tokens earned by leveling up or alternatively pay for apex coins

If you do not have enough tokens or don't want to spend your hard earned cash on purchasing apex coins. All that is left to do is keep playing, level up as with each level you gain tokens. Eventually you will be able to unlock all Legends, it just requires some time investment.