US citizens who want to tour the White House can arrange it through their Congressperson. However, international visitors who want to tour the White House can make a request through their embassy.
Tours are only for groups comprised of a minimum of 10 people but your embassy may be prepared to try to group you with other tourists from your country to make it possible.
This is the information I got from the New Zealand embassy in Washington in February 2010.
START:”The Embassy can submit tour requests for New Zealand nationals and their guests visiting Washington DC. The self-guided tours are available from 7.30am to 12.30pm, Tuesday through Saturday and are assigned on a first come first served basis. Please supply for each person wishing to visit the White House:
Date of Birth
Required visit date:
Contact detail just prior to the requested tour date (email and telephone number as well as the name and telephone number of your hotel in Washington DC)
Unfortunately, submitting a request doesn’t mean a tour is guaranteed, as there are limited tours available. Tour approval can often be last minute so you may not hear until very close to the tour date.
The Embassy keeps a list and tries to make up a group of ten. If we can’t, then we are unable to put in the request. Just supply the details of your passport etc and we will notify you one way or the other nearer the time.”STOP
Non-US citizens can tour the US capitol building (free) without arranging it in advance.