My best advice on how to do it would be to watch some YouTube videos. What I will strongly advise against is using contact cement from an aerosol can. I don't know of any that have held up past the first or second summer, if it even lasted throughout the reinstallation. I bought a gallon a DAP Weldwood adhesive and used a cheap Harbor Freight spray gun on my air compressor to install a fiber-backed outdoor upholstery vinyl (HEAVY!) headliner in my Jeep XJ. Four years later, it still looks like the day I installed it.
If you don't wanna invest in all the tools and materials to do it the correct and permanent way, you could split the difference by removing the panel, stripping off the old material and bringing it to a shop to re-cover it. Most of the labor is the removal and installation, so just having them cover it should be considerably cheaper. It'd be a professional job and you wouldn't have to buy all this stuff that you'd likely never use again.