The information provided by @pnuts is correct, according to various web sites, although absent from the Ministry of Home Affairs and Immigration web site.
Getting an extension requires a visit to its Windhoek offices in the Cohen Building on Kasino Street (at the corner of Independence Avenue). Kasino Street is between Independence and Luderitz Street in Windhoek Central.
The Cardboard Box Namibia organization gives a good summary (and current in 2016):
Please note that the following information is correct at the time of writing (and is updated frequently), however these things do change frequently so it may be worth checking the current visa requirements before travelling to Namibia.
All visitors require a passport to enter Namibia. This passport must be valid for at least 6 months beyond the intended stay and have sufficient pages for entry and exit stamps. All visitors must also have a valid return ticket.
Minimum Requirements for Tourists exempted from visa requirements to enter Namibia:
- Be in possession of a valid passport which is valid for at least 6 months beyond intended departure date from Namibia
- Be in possession of valid return / onward air ticket or proof of other means of transportation enabling him to leave Namibia
- Entry into Namibia will be permitted for a maximum period of 90 days, (extension possible on application to The Ministry of Home Affairs during stay in Namibia.)
Visitors from the following countries do not require visas for stays of up to 90 days:
Angola, Austria, Australia, Belgium, Botswana, Brazil, Cuba, Canada, France, Germany, Italy, Ireland, Japan, Kenya, Liechtenstein, Luxembourg, Russia, Spain, Switzerland, UK, USA, Mozambique, New Zealand, Portugal, Iceland, the Netherlands, Malaysia, Singapore, the Scandinavian countries, South Africa, Zambia and Zimbabwe.
In requesting an extension, you may be required to show your onward ticket, or evidence of sufficient funds. While no mention is made of the cost of an extension, if any, the current visa handing fee is N$80 ($5.75 US), and N$ 390 success fee ($28.00 US) might be charged. Perhaps fees could be waived as your extension would be for just one additional day.