I squared the ends and drilled holes on each piece that lined up. About 5 holes for a 1" belt. Then,I cut grooves on the FLESH side of the leather(which runs against the pulley. Do not disturb the HAIR side-that is where all the strength is. Lace the belt together with heavy gauge copper wire. Make sure that on the underside of the belt,the wire lays in the grooves. This keeps the belt from going clack every time it goes around,because the wires do not touch the belt. Just twist the ends together so that they do not touch the pulley and clack. Lightly hammer the lacing a bit when done,to seat the copper in the grooves well. Don't beat it to death.
Old timers also sometimes glued the belts together by skiving long,mating angles on each side of the belt. They glued the belts together with a mixture of TANNIN and hide glue,which came close to being the same stuff the belts were made of. I don't think the tannin is really necessary. I'd recommend liquid hide glue as it is more flexible than hot hide glue.
Belts stretch so much,I really recommend lacing them with the copper wire. Then,you can more easily cut the belt shorter and re lace when needed.
The man made belting will be less trouble. Rubber impregnated with fabric will not stretch like real leather. It can be laced the same way.