If you missed a traffic court or contested hearing, this is a civil hearing and the court cannot issue a warrant. Instead, the court finds the ticket committed, notifies DOL, and then sends you the bill for the fine (or to collections.) However, if you missed a criminal court hearing, the court can and usually does find that you failed to appear and issues a warrant for a specific sum of money. The warrant can be posted either in cash or bond, however. If not, the court will normally bring you in front of a judge the next judicial day to address the warrant.
You may want to contact the court where the warrant issued and see if they have a procedure in place for getting a warrant recalled. It usually entails showing up for court on a designated day and time and telling the Judge why you missed court. If you choose to turn yourself in on the warrant, I suggest you do so on Monday through Thursday. That way you will have your first appearance no later than the next day. If you choose to go to court or turn yourself in, the court will decide whether to release you on your own recognizance or impose a bond. That decision will be based primarily upon your ties to the community and your prior record of appearing or not appearing for court. I suggest you retain a criminal defense attorney. If you cannot afford one, you will be able to request a public defender after the warrant is taken care of.
Never ever ever turn yourself in on a warrant. What you want is a court date to quash the warrant. If you just turn yourself in to the jail they can hold you for a long time. You will get a court date soon after getting into jail where they will consider your release conditions. If the warrant issued then they might view you as a flight risk and put some bail on you. Then you will be held until you post the bail. If you can't post the bail then you will be held until your next court date. If you want a trial then you will be held until your trial date. You have a right to a speedy trial within 60 days. That is a long time to wait in jail.
What you want to do is hire an attorney. You might be able to get the warrant and the charge taken care of on the same day if your attorney can get a deal worked out. An attorney can help you get that warrant quashed. If you can't afford an attorney then you should apply for a public defender to help. If you can't afford an attorney and you don't qualify for a public defender then you should call the court and ask them help you quash your warrant. The last thing you should do is walk into the jail and ask them to take you in.