In your own vehicle
South Luangwa's network of roads is not as extensive as you might expect. A few all-weather roads (mostly graded gravel) have been built in the park around the Mfuwe area – accessible over the main bridge into the park. These are the only roads that can be relied upon during the wet season.
Elsewhere, the park has seasonally passable roads that are (optimistically) marked on some of the maps. Such tracks follow both banks of the Luangwa, north and south of Mfuwe, and a few penetrate westwards into the park. In the areas near camps, there are numerous 'loop' roads, which leave these main tracks and return to them. These are just side roads for game viewing, and trying to be precise about their position is pointless – they are usually made simply by the passage of a few vehicles, and will disappear again very swiftly once the vehicles stop.
Note that if you are driving your own vehicle around the park then you are limited to being in the park from dawn to dusk. You are not allowed to stay in and drive around after dark, as only the local safari companies have licences to conduct night drives. (Note also that the Nkwali pontoon marked on many maps opens 1 June to 31 October and is not for use by private vehicles.)
Without a vehicle
If you do not have a vehicle of your own, then you should organise your camps or lodges before you arrive. If you haven't done so before you arrive, then you may be limited to the Wildlife Camp or Flatdogs. If your budget is higher, then you might consider stopping at Moondogs Café (by the airport) and asking them to radio a few of the more upmarket camps to see if any have space left. This is unusual, and don't expect bargains (you won't find any), but it is a real waste to get all the way here and then not make the most of the park. So if you can, splash out on the best place that you can afford.
Two different maps of the South Luangwa National Park are available in Lusaka. One showing South Luangwa and Luambe National Parks was compiled for the National Tourist Board, and is useful in giving the general scheme of the area's roads. Otherwise the information on its reverse side is fairly dated, and so not very valuable.
A second very different map concentrates on just the South Luangwa National Park. This was produced in 1989 using aid donations and shows the landscape and vegetation in considerable scientific detail; it's a scholarly work. Its reverse side details the various land systems in the area: the different combinations of land form, rock, soil and vegetation in the park. This is a fascinating map which has some of the camps marked, but only a few of the existing roads.
In the unlikely event that you need to navigate yourself at all, get both of these and consider also buying more detailed Ordnance Survey-style maps available from the Surveyor General's office in Lusaka. Such detailed maps (preferably together with a GPS and good local guide) would be essential for visits to Luambe or Lukusuzi.