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.
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.
In winter, try cross-country skiing along the Sviaga river, in summer take a boat ride over the reservoir.
The city's main shopping centre 'Tsum' is basic to say the least but does offer some basic shopping.