Lithuania has three international airports. Vilnius International Airport is the largest one, accessed both by national carriers and low-cost carriers. Kaunas International Airport is a Ryanair base with little other services. Palanga International Airport offers several routes, but flying from there is generally more expensive due to lower competition.
All airports are connected to city centers by public transport and from there you can catch inter-city buses. In Kaunas and Vilnius, you can catch inter-city buses to major other cities directly at the airport, but the options are limited. Unfortunately, all public transport comes to halt during the nights and so it won’t help you in the case of early departures or late arrivals.
Lithuanian airlines had been having a bad luck with five of its carriers (Lithuanian Airlines, Air Lithuania, Amber Air, Star 1 and Air Lituanica) went bankrupt and were liquidated.
Generally, Western Europe and Southern Europe are both well-served by air routes from Lithuania (the latter especially so in summer). A few Eastern European cities are also served but going anywhere beyond that (e.g. Balkans, America or Asia) you'll need a transfer.
Lithuanian boasts an extensive network of open general aviation airfields, with 25 of them available across the country (flights from the Schengen area countries are permitted to land in any of them).
If you enter Lithuania by car it is trivial from other countries that signed Schengen treaty – Latvia and Poland. There will be no customs or passport checks. However, the waiting times on borders with Russia and Belarus may get long (several hours).
You can also reach Lithuania (Klaipėda port) by DFDS car ferries from Germany and Sweden. The duration of the journey is at least 15 hours. Cruise ships also dock in Klaipėda during Baltic cruises in summer.
The possibilities of entering Lithuania on rails from the West are rather limited due to Lithuania using broad-gauge instead of the common gauge. As such service to/from Bialystok (Poland) is the only train service going westwards. On the other hand, getting by rail to/from cities like Moscow, Kaliningrad, Saint Petersburg (Russia), Daugavpils (Latvia) or Minsk (Belarus) is easy (albeit slow). There is no passenger rail service between the three Baltic capitals.
There are international buses leaving for Western cities, but with the advent of low-cost airlines, the number of them severely dwindled. Buses remain a popular option for shorter distances, however, such as Vilnius-Riga, Vilnius-Warsaw or Vilnius-Minsk.