There are several ways to get to Siwa:

Air-conditioned coach buses from Cairo or Alexandria. These stop in the coastal town of Marsa Matrouh before heading to Siwa.
Bus tickets cost around $10 each and should be bought in advance as soon as you get to Cairo.

Minibuses to Marsa Matrouh/to Siwa. These only cost a few dollars but tend to be packed, sometimes reaching 20 people per van. For a group of four or more people, consider buying all the seats on a minibus. The bus service between Siwa and Matrouh is limited to two trips daily. 

Car rental (with chauffeur) The fastest and easiest option, but also the most expensive: about U.S. $ 170 one-way. One benefit to a private driver is being able to stop anywhere along the way. Consider stopping to swim at Marsa Matrouh or to visit the battlefields of Al Alamein.