If you meet the criteria of a milestone, you may claim it by paying 8 M€ and placing your player marker on it. Each milestone may only be claimed by one player, and only 3 of the 5 milestones may be claimed in total, so there is a race for these! Each claimed milestone is worth 5 VPs at the end of the game.
These are the milestones and what you need to claim them (besides paying 8 M€):
1) Terraformer: Having a terraform rating of at least 35.
2) Mayor: Owning at least 3 city tiles.
3) Gardener: Owning at least 3 greenery tiles.
4) Builder: Having at least 8 building tags in play.
5) Planner: Having at least 16 cards in your hand when you claim this milestone.