As long as the neck is smooth and scratch-free, you just rub it on with a lint-free cloth. You don’t want cloth fibres sticking to the finish, so do make sure the cloth doesn’t shed. I’ve bought lint-free rags from Amazion for this purpose, though I have also used good quality old t-shirt rags. I cut a small square to use about 10-12 cm sides, as you’ll want to throw the rag away after a single use. But let it dry in the open air before putting it in a bin.
TruOil gives off heat as it dries, and if you have say a complete T-shirt soaked in it, and crumple it up and put it in a bin, it is possible for the heat to build up in the middle and set the TruOil on fire. Almost certainly not going to happen with a single small piece of cloth, but still best to let it dry spread-out before binning, just in case.
The standard option for the fretboard would be to cover that in TruOil as well. This can be anywhere from a couple of thin layers for minimal protection, to a thick coating if you want a Fender-style finish. You’ll apply it over the frets, which will then have to be cleaned off them later. If you plan to level the frets, then that process will remove the TO. I’ve also seen scrapers made using a 6” round-headed nail with a small notch filed in the head with a round needle file.
The smoother the TruOil goes on, the less sanding you’ll need to do. I found that the TruOil in the bottle thickened with age and exposure to air when left open, so you can thin it with turpentine if you feel that will help. Just add a small amount at a time until you feel it’s runny enough, but I wouldn’t go above 50:50. The thinner it is, the thinner the layer it leaves will be, so you’ll probably want to apply more layers.
As always, don’t sand the edges directly, as it’s very easy to sand through on the fingerboard edges. If you want to ‘roll’ the fingerboard edges so they are rounder and feel more like a played-in guitar, then do that before applying any finish (if you don’t want a relic look).
You can just sand the finish with up to P1200 or P2000 paper (or grey and white Scotchbrite pads) and forego the polishing if you want a less glossy-finish that doesn’t feel sticky to the fingers.
My limited experience of TruOil shows that it takes a considerable time to cure really hard, at least a month, so if you want a really glossy finish, you need to wait before final sanding and polishing.
Some people have just waxed the fingerboard as they aren’t keen on the feel of glossy boards. This provides reasonable protection against dirt and sweat, but you’ll need to re-apply occasionally.
You could go all EVH and leave the fingerboard unfinished, but you do leave the board more open to drying out and getting very dirty. Also remember that he didn’t use the cheapest of Chinese necks, but good quality Schecter ones, so were less likely to warp or twist with temp and humidity changes. I don’t know if he ever replaced the necks at all, but I do know he was forever swapping parts in and out, so I suspect the necks may have been changed over the years as they wore.