The LFS cars above use dog boxes (not sure about the F1). IRL this is how you shift:
To shift up, You put some pressure on the shifter, release the throttle, then you'll FEEL you can move the shifter, so you slam the shifter into the next gear and get back on the throttle. You don't use a clutch. You could use the clutch but you'll just wear it out, it has no advantage.
As shotglass said, in a more advanced system with some basic electronics, you don't even need to get off the throttle, the electronics detect when you move the shifter, cuts the ignition and all you do is slam it into the next gear, with your foot flat on the throttle.
To downshift you do use the clutch, just like a normal box. You can use a bit of throttle when you get into the next gear, but that's for stablising the back end. You can do clutchless downshifts with throttle blip, but it's a very precise work, it isn't recommended and is usually associated with a bit of intervening electronics.
What doesn't work IMO is the way the upshift is simulated in the FBM, because you can't FEEL when you've selected the next gear, so I find myself trying to get into next gear and it works sometimes but not always. I have no idea when i'm supposed to get back on the throttle, can't even hear it. For me it's a very unrewarding uninituative system.
I would like to hear how other deal with it. I'm sure there is a way to shift fast without ever missing a gear.