As with most countries in the European Union, United States citizens are allowed to enter Poland without a visa for up to 90 days. This is strictly for tourism purposes; you are not allowed to work or live in Poland during this period. If you intend to stay in Poland for longer than 90 days, or take up gainful employment during this period, then you must apply for a visa. The expiration date on your passport should not be less than three months after the date of your planned departure from the country.
Those who hold European Union citizenship or citizenship from countries belonging to the Schengen Zone need only show their ID cards when entering Poland; no passport is necessary. Those individuals are allowed to stay in Poland for longer and work there without obtaining a visa, though they must obtain a residency permit before renting or buying property.
Citizens of the United States of America are not required to have a visa when entering Lithuania for tourism purposes. You are allowed to stay in the country for up to 90 days, within a six-month period. As Lithuania is also in the Schengen Zone, the same rules apply as for Poland with regards to travel in between member countries. If you intend to stay in Lithuania for longer than 90 days, or to work while you are in the country, then you will have to apply for a visa.
If you intend to live, work, buy property or start a business in Poland or Lithuania, then you will need to apply for a visa. The visa will then be pasted into your passport by the relevant authorities. While it is possible to apply for the visa once you are in the country, keep in mind that this is Eastern Europe, where there is a lot of bureaucracy you will have to deal with. You can save yourself much time and effort by applying beforehand through Poland's consulate and/or Lithuania's embassy in the United States.
Consulate General of the Republic of Poland in New York
233 Madison Ave.
New York, NY 10016
212-561-8160
polishconsulateny.org
Embassy of the Republic of Lithuania to the United States of America
2622 16th Street NW
Washington, DC 20009
202-234-5860
ltembassyus.org