The exploit as described in the original post on YouTube is a bit vague and may not work on the Xbox or PS2 versions. I'll put it on this board for now.
Before attempting the glitch you will need the vehicle that you want to customise in the San Fierro safe house garage in Doherty.
The first step is to start any side mission (Trucking, Vigilante and Courier works) and head straight towards San Fierro airport to the flight booker. Leave your vehicle and enter the flight buying GUI. Wait until the warning for the timeout is at 5 seconds to enter your vehicle before the mission ends, and then buy a plane ticket to any of the 2 islands.
If the glitch succeeds the side mission should fail and CJ should immediately exit the plane, despite not being able to in normal circumstances. The 'Press F to skip flight' prompt will still be on the screen but CJ will be on foot and mobile.
Jump back from the airport to Doherty as fast as possible (Do not run when going to Doherty, this will break the glitch) and get in a traffic car. Reverse all the way into the Mod shop.
When the mod shop appears, select the list of Wheels and either wait until the flight that you tricked the game into thinking your still using into the end of the flight, or skip the flight by pressing F. You should now be in blue hell and CJ will be mobile again, with nothing visible but the airport gate. (Do not buy anything and stay on the wheel menu.)
Navigate yourself through the gates and into the invisible world until you arrive back at Doherty, only shown as a small section in the abyss. Doherty should be easy to find as its the only visible area once you walk through the gates and head north-east from there.
Get inside your desired vehicle inside the garage. The vehicle(s) may be invisible but all vehicles inside the garage will still be enterable. With the selected vehicle, drive into the Mod shop.
This is when you can start modifying your vehicle. This can be used on any land vehicle that you inserted in the garage but crashes may occur. ALL options for customisation should be available, wheels, nitro, body mods and color can all be changed.
Once you are done modifying the car to your choice exit the garage. The world will appear as normal and you wont be in Blue hell anymore but your camera will be glitched, stuck above the garage. Simply enter a nearby car and your camera will be back on CJ.
Head to the garage which you retrieved and customised your invisible vehicle from before and your changes will already be inside.