Ulyanovsk (Russian: Улья́новск ool-YAHN-uhfsk) is the capital and principal city of Ulyanovsk Oblast. Note that unlike Kazan, Ulyanovsk is not a common tourist destination for foreigners, and it may be difficult to find people that speak English.
Ulyanovsk Baratayevka Airport is 9 km from the city center, on the western side of the Volga (the same side as the city center). As of January 2018 it is still closed for renovation.
Ulyanovsk Vostochny Airport is 28 km from the city center, on the eastern side of the Volga. The trouble with this particular airport is that it doesn't have any means of public transport, connecting it to the city center. Be prepared to order a taxi (there are unlicensed taxi-drivers waiting in front of the terminal after most of the flights, but their rates are much higher than avarage).
UTAir  has two daily return flights from Ulyanovsk Vostochny (until Baratayevka is open) to Moscow Vnukovo.
RUSLINE Air Company has two daily return flight from Ulyanovsk Vostochny (until Baratayevka is open) to Moscow Domodedovo.
Wikitravel has a guide to Trans-Siberian Railway.
The train takes you here from Moscow (from Kazanskaya train station) in approximately 16 hours or from Volgograd in about 20 hours. Train tickets range from RUR 500 (USD 20) to RUR 5,000 (USD 200) one way, depending on the amount of privacy and comfort. Ulyanovsk Main Station is located 6 km from the city center. However, a tram stops right outside the Station and will take you near to the city centre (north, or left as you walk out) for RUR 16 (if you use Pay Pass) or 17 (if you pay by cash).
The bus station (autovokzal) is located about 2 kilometres west of the city centre and has buses to and from many regional destinations, including Kazan and Nizhny Novgorod. From the station, it's about a couple minutes walk north to the main street and tram station. Take the tram towards the city centre (to your right), or look for one of the many Marshutkas that say K. Marksa (Karl Marx Street).
Ulyanovsk has an extensive public transportation network that includes buses, trolleys, and trams. It is very affordable (20 RUR ~ $0.60 per trip), but congested and may be quite confusing. You won't find any route maps or schedules, neither at bus stops nor in buses.
The easiest way to get around. It's best to download phone apps for the main taxi-operators, like "Yandex Taxi" or "RuTaxi", as they have English interface and you can choose the car type or request an English-speaking driver. Also the prices there are fixed and much lower than the ones you might get if you try to get a taxi on the street.
You can find trams on the right bank of the Volga River - where most sights are located. Though not very comfortable, they are the cheapest and the easiest way to navigate Old Town/City Center.
As of January 2018, one-way ride costs RUR 16 (if you use Pay Pass) or 17 (if you pay by cash). The tickets are sold by tram conductors/fee collectores, who usually don't speak English, so that may be quite a problem.
Tourists can use the tram to get to the four consecutive stops in the old town with the main sights: Lenin Street (Ulytsa Lenina), Goncharov's House (Dom Gontcharova), Lenin Square (Ploshad Lenina) and Lenin Memorial Center (Memorial Lenina). Bear in mind though, that they can get pretty crowded during peak hours.
By private mini-buses
The most common type of transport. They connect two sides of the river Volga via the old Emperor's Bridge (Imperatorsky Most). They range from old Russian Gaz mini-vans to relatively comfortable Ford mini-vans.
If you don't speak Russian it's best to avoid them, because their routes are really confusing, the drivers do not speak English, buying a ticket is counter-intuitive and the whole experience might ruin your day.
There are a few bus routes that also connect to sides of the river. The problem is that they are few and far between. The process of buying a ticket is similar to trams, though the conductors don't have Pay Pass terminals yet, so the only option is cash.
These are used only on the left bank of the river and, as there are no sights worth mentioning or visiting (this part of the city was mostly built in the second half of the 20th century), you'll probably wont use or even encounter them.
As the home town of Lenin, it's worth visiting the Lenin Memorial Centre and Gardens and museums based in his former houses. There is also a museum dedicated to the poet 'Goncharov' and the war memorial at the end of the main street 'Ulitsa Goncharova' offers breathtaking views over the Volga. Aside from this, the city centre, which is centred around the intersection of ul. Karla Marksa and ul. Goncharova, and the adjacent area along the Volga River is very compact, clean, picturesque, and easily navigable.
In winter, try cross-country skiing along the Sviaga river, in summer take a boat ride over the reservoir.
Also, in the winter of 2016, Ulyanovsk hosts the World Bandy Championship. Bandy (referred to by Russians as simply "ball hockey") is the precursor sport to ice hockey, where teams play 11-a-side on a rink the size of a soccer pitch. It is still very popular in Russia and some European countries, and is worth a look, especially for ice hockey enthusiasts.
The city's main shopping centre 'Tsum' is basic to say the least but does offer some basic shopping. A mall called 'AQUA' has opened in the old part of the city and houses several russian and western brands. It also has a ferris wheel and a riverside promenade besides several restaurants and a food court.
There are many drinking establishments in the area of Goncharova and Karla Marksa.
There are two hostels, Apelsin and Like, that are across from each other on ul. Federatsii just past Molochnyy per. Both offer similar dorm style accommodation for about RUR 500 per night. Note that the staff does not speak English, and there may be curfews to be aware of if you plan to stay out late.
City center is generally safe, both during daytime and in the night hours.
It is best not to venture beyond it if you don't speak Russian or don't have any local friends to help you get around. Some of the city districts are associated with street crime and, though not dangerous per se, are not the best places to visit alone, especially at night. As with most such neighbourhoods, they don't have any specific sights you might want to visit or hotels to stay in, so you have a pretty high chance of never encountering them.