To edit an existing mission you've created, click on the Missions Panel and select Custom. This will detail the missions you have created. Click on the mission you wish to edit.
Note: When you edit an existing mission, this will restart the mission history (change pay, # of plays, and XP) and therefore treat the mission as a new mission. If you are only making a correction to a spelling error, not changing a task, this is not considered a modification to the mission and the mission history (payout, plays, XP) will stay as is.