If you plan on framing your completed cross-stitch project, it's a good idea to hand-wash first to remove oils from your hands and any other dirt.
Place a terrycloth towel next to the sink and transfer the project to the towel. Do NOT wring or twist your project! Instead, roll the towel up with your project inside. Press down on the rolled towel to absorb the excess water.
Remove your project from the rolled towel and place face-down on a dry towel. Carefully iron on a low to medium setting (depending on fabric) until completely dry.