Tourist structures are the Galaxy Motel, Pisa HotelPassenger Terminal, Stadium  and Crater Park. Others will be added later.  These buildings increase your Tourism capacity limit.

Just like regular population, tourists eat food, drink (H2O), breathe (O2) and exhale (CO2). So your resource ratios will be affected by tourism.

You must build up your tourist numbers by running Charter and/or Scheduled flights.

Charter flights are run from the Market in the Landing Field.  Tap on 'Tourists' in the list and you will be presented with the Charter screen, then proceed as usual.  

Scheduled flights are automatically run from the United SpaceLines building which fetches 20 new tourists every 504 seconds (21 days). You are yielded ticket revenue upfront at current market prices.

Every day (24s), your tourists yield $100 each.  Also every day, 5% of your tourists automatically leave your base to return home.  On average, a tourist will yield 2000$ during its stay on your moonbase.  So you must keep getting new tourists if you want to keep your Tourism numbers up.

For the most part, tourism is not a mandatory activity for your base with the exception of one tutorial activity. Once you are finished with that particular activity, it's up to you to decide to continue to support tourism.