Where an exchange agreement exists, the DMV may ask for the original license, proof of identity and residence, and a translation of the license if it isn't in English. Some DMVs specify who may translate, or accept only an International Driving Permit or a translation from a consulate, so read the requirements carefully before ordering. Where there's no agreement, the foreign license may still be useful as evidence of driving history, though you'll usually need to pass the tests.
As a new resident, you're usually expected to get a state license within a set period after moving, and that period varies by state. We can't tell you your state's deadline, but your DMV can, and it's worth knowing before your insurer asks.