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.
UTAir  has two daily return flights from Ulyanovsk Baratayevka to Moscow Vnukovo. (Feb 2013)
Volga Dnepr Airlines  has one daily flight from and to Moscow Vnukovo airport.
POLET Air Company has one daily return flight from Ulyanovsk Vostochny to Moscow Domodedovo. (Feb 2013)
AviaNova  has flights from and to Moscow Sheremetyevo on Sunday, Monday, Wednesday and Friday. Flights on AviaNova start at 799 rubles each way not including fees.
Ulyanovsk Baratayevka Airport is 9 km from the city center, on the western side of the Volga (the same side as the city center).
Ulyanovsk Vostochny Airport is 28 km from the city center, on the eastern side of the Volga.
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 14.
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. Fee collectors usually don't speak English. Express buses and semi-private van routes are more comfortable and more expensive. Taxis are not expensive (9 RUR — 0.20 EUR per km), and that's your best bet if you want to get somewhere (relatively) quickly, in (relative) comfort (almost all cars are old Russian ladas or over 10 year old non-Russian cars), and without much hassle. They are also most likely to have English speaking drivers (one in 1000) and superloud Russian pop music.
Getting between the banks of the Volga is a problem. There is a two lane bridge connecting the banks and it's nearly always congested, so if you're unlucky, it can take a couple of hours. Most locals avoid going over the bridge if they can. There is a new four lane bridge due for completion in 2010 that is supposed to relieve these problems.
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.
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.