From the first building, you'll need to navigate through several outdoor screens and potentially another small building. Keep moving generally north and east. You'll encounter more guards, some with dogs. Dogs have a wider detection range, so be extra careful around them. Use the Binoculars to scout ahead and identify safe paths.
Your path will eventually lead you to a prison block. This area is typically heavily guarded. Look for a room with multiple cells. Gray Fox is held in one of these cells. You'll need to find a Card Key 1 to open his cell. This key is usually found in a nearby guard post or a small office within the prison complex. Once you have Card Key 1, approach Gray Fox's cell and use the key (equip it and press 'A') to open it.
After rescuing Gray Fox, he will provide you with crucial information about Metal Gear and the location of other captured agents. He'll also give you a Transceiver, which allows you to communicate with other support members like Miller and Diane. This is a significant plot progression point.