Windhoek is the capital of Namibia.
East towards Botswana, Gobabis, Windhoek Airport
Take a taxi from center (9 N$) or walk which will take you merely 30 minutes to Klein Windhoek. Get out at the Engen Petrol station. You got two possibilities here: Ask people either at Engen or Puma petrol stations or stand at the traffic lights just at that particular junction and approach the drivers while they are waiting. Especially getting to the Airport is very easy from that point.
North towards Swakopmund, Okahandja, Otjiwarongo, Zambia, Angola
The best spot is probably the ramp close to Katutura Hospital. Get a taxi for 9 N$ and tell the driver to stop at "Katutura Hospital / Highway to Okahandja" or if you're more into walking it`s a 5km walk. At the spot, do rather not join the other people waiting in the ramp itself as they are mostly looking for charged lifts. Try to stand at the traffic lights before turning right on the ramp and ask the drivers personally.
South towards Keetmanshoop, South Africa
From the centre you can take a 'taxi' (see Public Transport below) or walk. If you choose to walk, you should be prepared to walk 1–2 hours.
If you take a taxi you should look for one that goes to Olympia and ask to be dropped of at the last round about before the road to Marienthal or at the last petrol station depending on what you prefer.
The roundabout where the B1 is joined by the western bypass is the best place to hitchhike out as cars are very slow when they get out of the roundabout and they have a big area to pull over. Most people will go to Rehoboth from here.
To get here you can either walk although expect it to take a 1-2 hours or take a 'taxi' (see public transport) to Olympia and ask to get dropped of at the last roundabout on the road to Rehoboth. It should cost around 25 Namibian dollars from the centre of town at the time of writing (March 2013).
Another possibility is to get off a bit before at the petrol station and ask around although the vast majority there are just people going in town as the petrol station is actually in a suburb.
While the public transport network in Windhoek may seem complex at first it's actually about as simple as it is inefficient.
Basically there are NO buses at all and almost no minibuses. All there is are shared taxis which functions almost as a bus in the sense that they have semi-fixed routes which they follow. Although they do change their route to let people off at the door.
At the time of writing (March 2013) a standard fare with a taxi was 9 Namibian dollars and when you cross a border the price is going to double automatically. For example, a ride of Katutura to the center (a good 12 kilometres) will cost you 9 dollars while a ride from e.g. Southern Industrial area to the center (more or less 2 kilometres) will cost you 16.