Generally, a petition must be filed with the court in which the conviction first occurred.  It must often be verified.  Some courts require use of a habeas corpus or other post-conviction relief form, to ensure all proper topics are covered and to assist pro se litigants.  After some period of time, the court reviews the petition and determines whether a prima facie case has been established.  If so, it will issue an Order to Show Cause, directing the prosecution or attorney general to show cause, if possible, why the writ or relief should not be granted.  After that answer is filed, the petitioner generally has an opportunity to file a reply.

 

            When the pleadings are complete, the court will consider whether summarily to dismiss the petition, grant an evidentiary hearing, or grant the petition (if the pleadings do not establish significant conflicts of fact).  Some states allow discovery by the defendant as a part of this process.  If the writ is denied, it is generally possible to obtain appellate review, either by filing a new petition in the court of appeal, or by appealing the denial of the writ to the higher court.

POST CON RELIEF " HABEAS " REVIEW OF STATE CONVICTION IS LIMITED TO RECORD BEFORE STATE COURT
Cullen v. Pinholster, ___ S.Ct. ___, 2011 WL 1225705 (Apr. 4, 2011) (on federal habeas corpus review of a state court conviction, pursuant to 28 U. S. C. 2254, raising a claim of ineffective counsel, under 28 U.S.C. 2254(d)(1) the federal court is limited only to the record that was before the state court that adjudicated the claim on the merits).