There are several ways, depending on your preferences, the day of the week, and the time of day.
First off, if you choose to travel downtown, don't do it during rush hour, a standard common-sense tip for anyone who has never been in a large city.
Secondly, if you can visit, do it during the week, after about 10am through 3pm.
The various ways are:
Car - The only form of transportation where you have any say on your riding partner. Hopefully.
Light Rail - A train that runs above ground, not a subway. Well lit, normally patrolled regularly by guards/policemen/security people. It is fairly safe, as safe as any other public transportation.
MTA - or Metro. Subway, in other words. This is also clean, though I've never seen it actively patrolled, I've ridden it at almost all hours, and even exited at some questionable stations by accident. No harm (real or perceived) has ever come to me.
MARC - this is a Train. A real, commuter, sit-next-to-a-stranger-with-a-laptop-and-cell-phone train. BORING
Bus - The way most people who live and work in Baltimore travel. Not a highly suggested way of getting into the city. You would have to know the routes well.
Cab - Expensive, but doable.
Public Transportation Schedules and Fares here:
These are mostly if you are staying OUTSIDE of the city.
Once inside Bal'mer, you can get around the Harbor by:
a) Hoofin' it. The best way to check out some of the pre-fire architecture. Hint - Find the Coolest Building of ALL Time on E. Baltimore Street. Hint2 - Look UP, at night.
b) Cabs. Eh, why do that? Cab's are for Executives running late for a meeting. But if you insist, they are flaggable. Try to stay on Pratt St., Lombard St., Baltimore Street. Basically anywhere near the Aquarium, The Gallery, or the Inner Harbor. For Fells Point, anywhere on Aliceanna Street, President Street, or Broadway. For Federal Hill - S. Charles, Key, or Montgomery. Of follow the preppie looking college kids coming out of and going into bars. Lot's of them. bars and kids. lol.
c) Water Taxi - The best way for tourist, IMO. You get (for a GREAT price, $5 for the day) a bunch of coupons to use around downtown - giving you a great clue as to where to go and eat and drink. The water taxi takes you from the Inner Harbor to Fells Point, a smaller, less packed area a few blocks away from the harbor. Small shops, some more 'cultural boutiques' and a great coffee shop. Cobblestone streets and all. Everything from peircing and tattoos to specialty clothing boutiques. Pricing ranges from college student to Deans Wife.
If you are getting off a plane at Batimore/Washington International(BWI)airport. A shuttle from the terminal can take you to your hotel/motel, depending on the hotle/motel or ask one of the red-cap (people that handle luggage)for the shuttle to BWI rail station, take a MARC Train (it's cheaper than AMTRAK) get off a Baltimore Penn Station, go outside the train to get a cab into the downtown area.
Baltimore has Metro buses, subway, lightrail that can take you almost anywhere you want to go in Metropolitan Baltimore. If your in the downtown area, you could walk to a lot of places or go to one of the subway stations or check cashing establishments and pick up a $3.00 all day pass which you can use on the bus, lightrail and subway.