Climb into the vehicle you need to drive across the yard and start it. Drive as close to the yard as you can without driving onto mud.
Arrange for one or two helpers to bring large plywood boards. You can also climb down and do it yourself, although this will slow you down. The boards need to be wider than the vehicle's wheels, and long enough for both the front and back wheels to be on them at the same time. You will need at least four boards. Wider boards will distribute the weight of the vehicle over more ground; this will do less damage to the muddy lawn.
Lay the first two boards parallel to each other, with their short sides facing the vehicle.
Drive slowly onto the boards until both front and back wheels are resting on them.
Lay a second pair of boards end-to-end with the first pair, the same distance apart.
Drive forward onto the second set of boards.
Pick up the first set of boards and bring them around to the front, setting them down end-to-end with the second set. Continue driving forward and picking up the boards you have driven on as soon as your wheels are on the other set. The boards will provide a temporary wooden "road" across the mud. This works best with at least two helpers to pick up and move the boards as you drive slowly forwards.
Alert whomever is laying the boards when you plan to make a turn. They will need to point the boards in the new direction; making turns gently will ensure that you don't slip off the plywood as you spin around.