When a person is wanted by police in connection to a crime or misses a scheduled court date, a warrant may be issued for that person's arrest. The warrant allows police to arrest a person on sight and bring her before the court. If the person turns herself in, she is considered surrendering to the warrant.
When a person discovers he has a warrant out for his arrest, he has the right to turn himself in at a local police station, sheriff's office or state police headquarters. This is commonly called surrendering to the warrant. Law enforcement officers will take you into custody and you will be booked and fingerprinted. At this point, you may be released once a pre-approved bail has been paid and you have been given a new court date; or you may be brought before a judge who will decide if you should be detained or released on bail.
A person who surrenders to a warrant is usually looked upon with favor by both law enforcement authorities and the judge. It appears like you want to take responsibility for your action rather than fleeing from the police. This may mean the difference between being issued a bail amount versus remaining in custody until at least the next court date.
If you know you have a warrant out for your arrest, you should probably first contact a lawyer and seek his advice and council. He will be able to tell you the likelihood of being taken into custody, the trial procedure and your various options and choices. The main downside is a lawyer will cost money for representation.
Fugitive Safe Surrender
Some cities and counties participate in a fugitive surrender program that allows fugitives to turn themselves in at various participating sites including churches. A person has four days to turn themselves in at "fugitive safe surrender site." If they do not turn themselves in by then, the police along with other law enforcement organizations such as the U.S. Marshals Service will track you down and arrest you.
If a person is wanted by an outside country that wants to extradite him, the U.S. attorney general may issue a surrender warrant that allows them to turn the individual over to the extraditing country for prosecution.