The standard advice for travellers in the developing world is to carry most of their money in travellers' cheques. Uzbekistan, however, is an exception as they are almost impossible to change outside the largest banks in Tashkent.
You will need to carry most of your money in cash. US dollars are the easiest to exchange and transport, though someone can usually be found to exchange euros, roubles or, at a push, sterling. Divide your money between multiple locations about your person and carry a dummy wallet with just a few dollars and some old supermarket loyalty cards as a decoy for pickpockets and anyone attempting to extract a bribe.
Uzbekistan has very few ATMs, and almost none outside of Tashkent, probably due to the logistical challenge of restocking them after every other transaction. Those ATMs that do exist are often in the lobbies of larger hotels and dispense either dollars or som. Some banks have a relationship with Visa, others with MasterCard. You'll need to look at the logo on the machine to see if your particular card will work.
If you run out of cash in a smaller town, banks will often advance you cash on a Visa or MasterCard, or you can receive Western Union, MoneyGram and other money transfers.
Uzbekistan until the very recently (Sept 2017) had two exchange rates: the official, government-controlled rate used by banks and businesses who have to report their currency exchange transactions; and the much better street (or black market) rate used by everyone else. However, they liberalised the exchange rate and the officil rate is now close to the one of the black market. As of Sept 2017 the rate was 8000 sum for 1 USD.
The Uzbek sum, worth 100 tiyin, is available in notes of 100, 200, 500, 1000, 5000, 10 000 and 50 000 proudly bedecked with Uzbek heroes and architecture, and trading now at around 8000 sum to the $1 US dollar in Sept 2017. Elsewhere you find the Kazakh tenge, Kyrgyz som and Turkmen manat and Tajik somani.
Banks are now more or less everywhere in Uzbekistan and, providing they have sufficient cash behind the counter, all of them will change dollars, euros and roubles at this rate. You will need to show your passport and sometimes the customs declaration confirming you brought the currency into the country in the first place. The cashier will stamp the declaration and list the amount of money changed. If you need to change less common currencies (including the Swiss Franc, CHF), you will need to take them to a branch of the National Bank of Uzbekistan.
While the US dollar is Uzbekistan's alternative currency, be circumspect in public as it is not legal tender. Bring it in cash, preferably in crisp and new bills and in a mixture of $100 bills (large bills get the highest rates) and small change (useful for paying for souvenirs and small items at B&Bs). Cash can be swapped for sum at hotel exchange counters and some banks. It's important to remember that you must declare your travellers cheques on your customs form on arrival; otherwise you won't be able to change the cheques at a bank. Credit cards enjoy growing acceptance and are ideal for emergencies, though the lion's share of the country's usable ATMs are in Tashkent. The National Bank of Uzbekistan supplies dollars for credit cards and traveller's cheques at most of its branches around the country. Local costs remain low by Western standards, other than at tourist-price hotels. With the largest sum bill retailing at around US$6 you can expect to receive a brick-sized wad of money when changing more than US$100. You'll need a carrier bag of cash to afford a flight ticket out of the country, even though the government introduced new 10 000 and 50 000 sum banknote into the circulation as of 2017.
A black or free market exists throughout the country for US dollars and, to a lesser extent, euros. Guesthouse owners, shopkeepers and bazaar moneychangers all exchange money. But with the official and black market rate are nearly the same now it just makes no sense to use a black market. Changing money on the free market is technically illegal so if you do decide to change, restrict your conversions to guesthouses or shop owners rather than the ever-shifting bazaar. Uzbek police are generally not interested in moneychangers but there's always the chance that the person you're changing with is in cahoots for a shakedown.