Either one. You'll find people that believe one way is better than the other but both work. I lay mine down but that doesn't mean you need to.
You probably don't want to use a turner to keep them upright. They make a mess when they hatch, those turners can be hard to clean up, especially if it is a type with the motor in there. Many turners have sharp corners where legs, wings, or necks can get caught.
Most people that stand them upright use cut-out egg cartons. They trim the cups so the eggs can breathe better and it's less likely the carton can interfere with the chicks hatching.