How do you damp proof around openings in a single skin masonry wall?

If I understand your question correctly, you don't normally put damp proofing around a window or a door. As long as you put a vapor barrier behind the timber cladding and finish off the wood work up to the edge of the opening you shouldn't have a problem. If you think it could be a weak spot, you can paint the opening with bitumen emulsion liquid. On the inside, you should put insulated plaster board right up to the frame in order to avoid getting cold spots. If you have a cold spot, this can lead to mildew problems. If this is an old shed, I am assuming there is no insulation in the floor, so I would suggest insulating the floor as well to prevent the floor from radiating cold - and sweating when you put heating in the room.

If you buy a roll of 6" damp course you can run it around door frames and windows to prevent damp from penatrating the frames .

There is a few ways you can go about this you can get water proof seal it comes in tins at the merchant you just paint it on. Make sure windows and doors are well siliconed in. Or you could have the external rendered.

The windows and door require a good quality sealant to be applied. The situation that you describe should not occur from direct rain water. The problem could be because the brickwork is old, perished and allowing the water through. The rainwater is splashing off slabs and soaking the brickwork. Gutters or roof may be leaking. Condensation can be the problem inside the building if cold bridging is happening.