Visitors (except from the CIS countries) require visas and passports valid for the entire duration of their stay. Visitors from some Western countries no longer have to present a 'Letter of Invitation' (LOI). However, this leniency does not apply to Dutch citizens. The Uzbek government seems to be restricting entry to those from non CIS countries and is making the visa process more difficult. You can get an LOI from travel companies when they make hotel bookings for you. Find out from your local travel agent. The LOI will probably cost 30-40 USD for a short stay. For up-to-date information, check the website of the Ministry of Foreign Affairs.
US citizens who do not wish to go through the trouble of dealing with the red tape themselves can count on the professional services of Travel Visa Pro to speed things up: Apply for Uzbekistan Visa Online (service starts from $39). If you need to renew, add pages, change name, or just get a new US passport, you can Apply for a New US Passport here.