Anyone can join an open game. In the Android client, they are listed in Open games. Games found using the Lookup item in the main navigation can possibly have filters preventing the viewing player from joining.
When joining a preference-based game, the player will be asked to rank their favorite nations of the variant of the chosen game. The server will use the Hungarian algorithm to maximize the total rank of the selected nations.
After all necessary players have joined the game it will automatically start. Depending on the popularity of the variant and the availability of players, this can take several days.
Note that games with very short phases will probably require constant monitoring. Players are better off removing themselves from unstarted games rather have them start (and run through many phases) when they are not available. Missing all the phases of a quick game is an easy way to damage your reputation.
It is also possible to create games with very long phases (up to 30 days). Some players may enjoy the nostalgia of a postal-diplomacy environment while others may find it infuriatingly slow.