Transportation in Montevideo is very complicated for foreigners. If you want to get around by public transportation, you can only rely on buses. An alternative are taxis and Uber.
There is no rail transportation in Uruguay whatsoever. That also means that there are no trains, no trams or anything alike in Montevideo. Instead, the only options to get to the city by public transportation are long distance buses, airplanes and ferries to Buenos Aires. In the city itself, there is not much more variety as there are basically just buses to get around.
There is one great article about buses in Montevideo in English. I’d recommend following this guide if you want to get around Montevideo by public transportation. My experience is that it is really tough to get an idea of the whole system. There are dozens of bus lines, but not all buses are operated by the same company. Thus, the public buses look different.
There is a sign with the destination, but there are no timetables whatsoever. If you are looking for a route from A to B, I’d recommend using the official website (in Spanish), which has a journey planner. The buses themselves are quite modern and relatively easy to use. You are paying the fare at the driver. Yet, without a basic knowledge of Spanish, you might have a relatively hard time. Nevertheless, the buses will get you to your destination safely.
The alternative to buses in Montevideo are taxis. Besides Uber, this would be my preferred means of transportation in Montevideo. Compared to European or American standards, taxis in Montevideo are quite affordable. However, they are not really cheap. The typical charge per kilometer is approximately 20 UYU (~ 0.7 USD / 0.6 Euro). A ride from the airport to the city center is approximately 600 UYU (~ 21 US-Dollar / 18 Euro), for example. Taking taxis in Montevideo is considered safe and quite comfortable. Yet, you should be aware that most taxis don’t have an air conditioning. Still, I’d prefer taking a taxi over a bus in Uruguay. Yet, you should always make sure that the taximeter is used.
My personal preferance for transportation in Montevideo is Uber. There are not too many drivers in the city, which means that you have to wait sometimes. However, Uber is very safe and reliable in Montevideo. Plus, the rates are lower than for taxis and communication is not a problem, even if you are not speaking Spanish. Other than that, there are a couple of touristic transportation options in Montevideo, especially in high season. This includes a hop-on-hop-off tour by Buquebus, the ferry operated between Montevideo and Buenos Aires.