Baltimore isn't a city known for its efficient public transportation system. However, there are 4 major options--bus, MARC train, Light Rail, and Metro subway.  Much of this info (fares, routes, etc.) can be found at http://www.mtamaryland.com. A one way bus or subway fare is $1.60, and a day pass with unlimited daily use on the bus and the subway is $3.50, a weekly pass is $16.50 and a monthly pass is $64. The buses run throughout the city and into Baltimore County.  The bus system is notoriously unreliable. If you have the misfortune to try and catch a bus when Baltimore City Public Schools let out, the students ride the buses and if it's full, the bus will keep right on going, and you're just out of luck, because you have to wait until the next bus, whenever that may be, and hope it's not full as well. This is most common between 2:30 and 4 PM weekdays during the school year.  The subway runs East-West only, and does not link up with either of the other two rail systems. If you're coming to Baltimore to go to Johns Hopkins Hospital, this is your best bet.  It runs from Owings Mills Mall, on the west side of Baltimore County off of 795, to Johns Hopkins Hospital, with stops in between. Here is a link to the system map. It is pretty reliable and a nice option if it's limited stops go where you need to go. 

Next, there is the Light Rail.  This is the North/South option, and again, it does not link up with the other two rail systems.  For a while now, either one half or the other of the light rail was totally shut down to double track the rails, and ridership has plummeted. You can grab this at the airport. 

Then there is MARC. The train schedules are mostly for commuters, and are unidirectional.  You can get to Frederick, MD, DC and WV using this rail system. 

The Charm City Circulator is a free bus that consists for two routes—the Purple Route which runs from Penn Station to Federal Hill, and the Orange Route which runs from Hollins Market to Harbor East. It operates 7 days a week, connecting parking areas, Amtrak, MARC, Light Rail, Metro Subway and buses are scheduled to run 10 minutes apart. The services also integrates with the Water Taxi Harbor Connector, extending free service on the water for select routes.

If you want an easy, convenient way to see the city and it surrounding areas, you're best bet is to rent a car.  However, if you're staying in only the city proper, you may be OK.  However, note that not one rail system goes into the highly regarded Inner Harbor area directly.  For that, bring taxi money and your walking shoes.  Driving around Baltimore is OK during non-rush hour times, but good luck finding parking!