All immigrants, documented or undocumented, are guaranteed certain constitutional rights. Basic rights such as freedom of speech, due process, and the right to a jury trial are granted on the basis of personhood, not citizenship.
The Supreme Court has gradually established that many constitutional protections apply to all people residing in the U.S. on the basis of legal language specifying persons, rather than citizens, in the Bill of Rights. Other rulings, such as Plyler v. Doe (1982), affirmed that undocumented immigrants are also viewed as persons in the eyes of Constitutional law.
In practice, laws vary widely, such as the expedited removal process enacted in the Illegal Immigration Reform and Immigrant Responsibility Act of 1996. Under this law, undocumented immigrants who have lived less than two years in the U.S. and are arrested within 100 miles of the border can be deported without a court hearing.