I didn't have a strap lying around and didn't want to cut up the leather to make one, so I took an old belt and turned it into a mandolin strap with minimal hardware.
It's detachable on one end, can be sized to fit anyone on the fly, and is sleek.
Step 1: What you'll need
1. Leather belt (any size-my length turned out to be almost perfectly 38 inches, hole to hole) Usually they are 1/2 inch to 3/4 inch, but mine's about an inch and it's served me well.
2. Basic hardware: be creative.
attachment method: this will be the ring that can connect the head to the strap. I used a 1 inch diameter ring, but you can just use string if you prefer
pinch mechanism: I used a nut and bolt, chopped down with a hacksaw to size. be sure not to bung up the threads.
3. Tools: a knife, hacksaw, wrenches if you need to tighten hardware down, bolt cutter for the ring, vise grips for bending the ring back in to where you want it. I also used a punch to widen the holes for the hardware, but a knife could do the trick.
Step 2: The Detachable End Thingy
Take the part where the buckle is held, using a knife, and turn it into the flat leather. there may be some rivets, which you can saw through quite easily. There's a nice little notch where the buckle clasp fits through, and it's perfectly sized for the mando cone. If you need, you can use a knife and cut a notch. Be sure to cut the notch towards the short end, as it's held together by the weight of the mandolin/tension from your body. Use a knife and cut any excess material away. Be sure to leave enough to be sturdy.