Coming from the states, there were a few things that shocked me about Uzbek transportation. For one: be wary of reckless drivers! Most drivers don't tend to stop for pedestrians, even though jaywalking is very common.
The most common car in Uzbekistan? A white Chevrolet. That's because there is a factory that monopolizes the market. In fact, 94 percent of the cars sold in Uzbekistan are Chevrolets (source). Most of them are white because of how hot it gets in the summer, and the lack of air conditioner in many cars. Windows down is a must.
Seatbelts, however, are not a must! Only the driver is legally required to wear a seatbelt, and I had some taxi drivers who didn't even wear them. Several times we also sat 4 people in the back seats, as opposed to 3. Though tight, it did save us the money we would've spent on 2 cars.
Speaking of cars, Uzbekistan has a convenient public transportation option: the Damas. These are blocky, white with an orange stripe, (you guessed it) Chevrolet vans that can seat up to 8 people comfortably, though once I did ride in one with 11 people.
Each Damas has a number or two on a large paper against the window. Each number represents a route. I wasn't able to find out online how to know which number to take, but asking locals around can help. Though that may be a hassle, the benefit is that the Damas is very cheap! When I visited, it was 1500 sums (or about $0.15) per ride.
Though there are Damas buses that can take you on longer trips (like one of the Top 3 Places to Visit), we took a taxi to get around. If you're staying at a hotel, they can usually set you up with a taxist, or you can use the Yandex Go app.
If you hitch a taxi, make sure you settle on a price before departing! Generally, a 1hr drive, to and from, cost us 300,000 sums (or around $30), which comes to about $15 each way. A short taxi ride to a nearby restaurant will likely be a 1000-3000 sums, or a couple dollars.
Another method of transportation that gets overlooked easily: walking! To get to the store and run errands, Uzbekistan if very pedestrian friendly (despite reckless drivers). Coming from a US suburb, I was surprised at how many people were on the streets. It was quite refreshing.
There are also metros and buses, but I unfortunately didn't get a chance to check them out. Hopefully this blog post gave you an idea of what transportation in Uzbekistan is like!