One can change the currency at many authorised (bank) kiosks at many places. The official exchange ratio you get is around 1700 soums per $.

In the airports and at banks you can exchange foreign currency at the official rate, which is a lot lower than the unofficial one.
The unofficial rate is around 2450 soums which one will get at many shops, money exchangers and hotels. Change only a small amount if you have to go by the official rate, or try to pay in Dollars.

Money exchangers can be found near markets. Ask the hotel or other travellers where they are. Usually, they can be trusted but you have to hassle for a good ratio (2450-2480 per dollar in July 2011) Taxi drivers (especially that are waiting at airports) can exchange some money too, but they usually give you a worse ratio (2200 per dollar). Do not change too many $ at one go, you have to carry bundles of soums, rather inconvienent.
On the other hand, try to pay all in soums because the price is usually better than in dollars. Always ask in hotels or agencies what the exchange ratio is that is applied when you pay. Sometimes, paying in Dollars might be cheaper (but not often).

When exchanging money, you may count it because the largest note is 1000 soums, and your money usually comes in packs of 50, so it's easy to put in 1000 or 2000 soums too little in a bundle. Beware that counting the money might take some time.
Euros (especially the 50 euro notes) can usually be exchanged at a rate as good as the Dollar (e.g. 3440 soums per 1 euro when the euro is 1.40 dollar).
It's usually no problem to exchange 20-50-100 dollar notes.

Forget about exchanging traveller's checks.

While leaving you cannot exchange the soums back into any other currency. So spent all the soums before leaving the country. Generally it is difficult to exchange large denomination foreign currency and crimpled foreign currency. So carry low denomination foreign currency.

There are atm's in Tashkent but they are scarse and often not working.  There is an ATM that gives cash in $ only on mastercard in Hotel Uzbekistan. Don't rely on them to get all your cash for the trip. Bring the money form abroad if possible.

Cash on  visacard/mastercard is possible at some banks in the center of Tashkent (near Timor square), Samarkand and Bukhara. Ask for dollars, soums only if you get a good exchange ratio.

When you want to use creditcards it's better to take two cards; one visa and one mastercard.

Take enough cash $/€/Soums with you outside Tashkent! Cash is king everywhere in Uzbekistan.

One thing about changing money in Uzbekistan is when you exchange for Uzbek Soms the highest denomination on the streets is usually 1,000 UZS that along with the 500 UZS are the most common banknotes making not having a huge handful of Uzbek Soms nearly impossible.however banks will usually be the ones that will issue 5,000 UZS Banknotes to you.That said it is best to carry crisp U.S. Bills in small denominations $ 1, 5, 10, 20. There has been problems to travelers there that USD Bills older then 2006 were not accepted. The Uzbek's are stern about this banknote exchange. the best thing to do  is Pay a bill USD then they'll give you better exchange rate when giving back change in UZS about 15-20% more from the official rate on the black market making very small purchases nearly free.United States Dollar is the best currency to have traveling thru Central Asia for exchange or acceptance more so then the Euro or GBP.