Once you are satisfied with your map, you can begin testing it. Please read this page, as test games have a few differences from normal games.
You can create a test game by changing your map mode to Testing. Then, create a Custom Game and switch the map category to "Testing Maps." Here, you'll see your map show up so you can pick it. It will only show up for you - other players cannot create games with your map until it is public.
Map testing games should be considered temporary. When your map is taken out of Testing mode, the games created using it will be automatically deleted. Currently, if you leave your map in testing mode, the game won't be deleted, however this is likely to change in the future.
Map testing should last fewer than 30 days. Maps may automatically revert from Testing to Development after 30 days and all games will be automatically deleted.
Testing games are really designed to be temporary games used to test a map to ensure it's fit for going public. For this reason, testing games cannot be ranked games and they cannot use open seats. Testing maps also cannot be used in tournaments.
When you are done testing, you can change the map back to Development to make further changes. Or, if everything looks perfect, you can make the map public.
Note: Map creators can use most member-only features when creating games on their own maps. For example, they can invite any number of players, use any luck percentage, and use custom scenarios in multi-player. This benefit still applies even after the map is public.