Also softcup you could buy at the store and you could leave them in for 12 hours
After intercourse you can lay flat on your back with you knees bent or you place your feet on the wall and prop a couple of pillows underneath of your knees so that the sperm don't have to fight gravity. There's not really any particular amount of time to lay there, but I typically went for about 5-10 minutes. Another suggestion I read about is to have sex before you go to bed, that way you are laying down immediately after sex and aren't walking around.