I live in the United States and am planning to travel to Poland. The only identification I have are my Mexican passport and my Mexican ID. Can I use just these to fly from the United States and enter Poland, or do I need other documents?
Mexican citizens do not need a visa to visit the Schengen area, which includes Poland, for up to 90 days for most purposes.
The answer therefore depends on the purpose and duration of your stay. If you are planning to work or study in Poland, or to stay for longer than 90 days for any reason, you will most likely need a visa to enter. If not, then the only official document you'll need will be your Mexican passport.
In addition to that, however, you may be asked to justify the "purpose and conditions" of your stay, which means that you may be asked to show that you have arranged for a place to sleep and that you have appropriate plans for spending your time in Poland. You can also be asked to show that you have enough money to support yourself during your trip.
To return to the US, you will need either a US visa along with your passport, or, if you're a permanent resident, your green card.