Public transport is your best bet. The closest Tube station is Charing Cross, which goes right to Trafalgar Square. Additional nearby stations include Leicester Square and Piccadilly Circus. If you're traveling by mainline train, the Charing Cross station is a three-minute walk away. Many buses will take you there as well.
There is much to see in the vicinity of Trafalgar Square. The National Gallery is where you'll find an extensive collection of Western European paintings from the 1200s to the 1800s. The National Portrait Gallery boasts the largest collection of portraits in the world. And St Martin-in-the-Fields is an English Anglican church that is located just minutes away.