just my experience with several headliners, including a couple made of vinyl, [those are a real treat to install !
] start at the rear and pull to the front, eliminating as many wrinkles as possible, then pull each section to the side, removing the remaining wrinkles.
a steam or heat gun will help tremendously when doing this.
several different blunt "tucking" tools will be needed as well, to push the material into the "teeth" that holds it in position on all sides.
leave as much material as possible on all sides until you get it "tucked" to your liking without wrinkles, then trim off the excess.
this can be done with or without the front and rear glass installed, although it is easier with the glass out.
just my life experience installing 10 or so headliners.
your mileage will vary.
and don't ask about installing a reproduction "one piece" ABS headliner............