You put the player in a queue and let them know you're looking for other players. Once there are enough players you start the game.

Matchmaking servers tend to have system that will host a game if none are available.  Often they'll be coupled with other systems like geoIP lookup to find someone who is "close enough", so you're not knowingly creating a match between Sydney and London, and skill-based ranking.

That is, pressing host always hosts, pressing join always joins, pressing find can either host or join but the client doesn't know which will happen.

From the user experience, they enter a game lobby after a few seconds that contains only themselves. If there are other players out there, they will likely join the lobby soon enough.