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If the moisture in your wall is coming primarily from the humidity in the air, try turning on your house's central air-conditioning system. Warm air retains more moisture than cool air, so chilling your room will lower the humidity significantly and make it easier to dry out the wall. If you don't have a central A/C system, try purchasing a portable or window unit. To help replace your house's old, moist air with fresh, dry air, try opening up any doors and windows located near the moisture damaged area. This will increase air circulation around the damp wall, speeding up the drying process.  Do not open your windows and doors if you're using a dehumidifier. For the best results, use this method during the day while the sun is out. This method may not work if you live in an extremely humid area. Wallpaper, wall fabric, and similar wall coverings will prevent air from reaching the wall itself, slowing down the drying process. In addition, soaked wall coverings can harbor dangerous mold and mildew, making them unsafe. Along with standard wall coverings, remove any other objects placed on your wall such as posters and floating shelves. If your damp wall houses any cabinets or similar furniture items, open up their doors and slide out their drawers. Not only will this help the cabinet dry faster, but it will speed up the overall drying process by increasing air circulation in the area.

Summary:
Turn on your house's A/C to reduce the humidity in the air. Open up your house to increase air circulation. Remove any wall coverings to increase your wall's ventilation. Open up wall mounted cabinets to help them dry faster.