On foot
In the center, especially in the historic part in Old Town Altstadt, everything is easily accessible by foot. Note that the city center is not the geographical center of the city.
By car
The street network is very good and many roads have been refurbished recently, especially in the city center. As in all bigger towns it can be a bit crowded during rush hours. There are many parking lots in downtown Dresden and it should not be a problem to find a place to park, despite on Saturdays when everyone goes to town for shopping. A number of automatic signs have been created, showing you the available number of free parking spaces, before entering the parking lots. Shops are open from around 10:00AM to 8:00 PM and you will see a lot of tourists and locals going shopping in the city center. Please beware of them when driving and note that this is the time with the fewest available parking spots. Car drivers might seem to be a little more aggressive than in other countries, but are usually more friendly if you don't have a local registration number.
By Bus And Tram
There is a combined system of tram called StraÃenbahn, bus and even train, but no subway. It works very well and connects all points of interest, but can be a little busy at peak times. Most lines run at night but with less capacity. This allows you to go out to most places or restaurants without the necessity to use a car, including to far flung places like Pillnitz. See Dresdner Verkehrsbetriebe DVB.
Best is to get yourself a Day Ticket or for families, a Family Day Ticket. It allows you to ride on all trams, buses, most ferries and trains except InterCitys and ICEs. It is relatively cheap and valid until the next day at 4:00AM. You can also get a ticket limited to an hour and some others, but Day Tickets are good if you are traveling around and not sure where you will be going and what you will be doing.
As with most places in Germany, the public transit operates on the honor system: you are assumed to have a ticket, and there are a few inspectors out spot checking. The exception is on the buses after 8PM, when the drivers are required to see all tickets.
Alternative Transport
Dresden has a lot of biketaxis (http://www.rikschataxi-dr...), mostly operating around the Old Town. They offer the typical short distance taxi service as well as guided city tours. Since 2007 there are also horse carriages that offer touristic sightseeing.
One can also make use of the many bus tour operators. Tickets for these tours can be bought around the old town from various points.
By bike
Bikes are the fastest thing in rush hour traffic if going a short to medium distance and if you're in good condition and not afraid of traffic and pedestrians. Bikes are also good for longer distances as they can be carried with a separate ticket in trams. There are many designated cycle paths marked red on pavements, or with a white bike symbol on a blue background and it is most times very easy to find a place to park your bike. But as anywhere else, always use a good lock!Much of the older streets of Dresden particularly in the northern, Neustadt area still have a cobblestone surface: not the most comfortable riding surface! Also, cobblestone is relatively slippery, compared to asphalt or concrete: care should be taken when riding in wet conditions.