Dresden has a number of car rental agencies from which you can rent a vehicle and see the city on your own. Alternatively, public transport being pretty good, you can use the city’s streetcars and buses. Both have a network spreading through most of the city, and are both fast as well as efficient. Taxis, though not as economical as buses or streetcars, are fairly inexpensive nevertheless. Fortunately for those on a limited budget, many of Dresden’s most popular sights are located within close proximity to each other, which makes it convenient to go around on foot.
If you’re planning to head out of town and see some of the outlying districts around Dresden, going upriver (or downriver, as the case may be) on the Elbe is a good idea. The Weisse Flotte’s boats ply regularly on the river, and touch most tourist attractions along the Elbe.