If you have to remove the needles (with some white face gauge installs you do and others you don’t)
If you do have to remove the needles make a drawing of the exact placement of the needles before you remove them<<< read that once more.
If you have to remove the needles and your kit didn’t come with some sort of needle removal tool you can use a regular dinner fork and slide it under the needle (did you make a drawing of where that needle was??) and gently pull or pry upward and the needle will release from the spline.
The only critical needle that you need to watch out for is the speedometer needle because it has a spring and will uncoil once you remove the needle. The spring helps hold the needle against the pin so that the needle will not bounce.
That’s about it the rest is installing the new white face gauge face, put the needles back on there splines exactly as per drawing that you made earlier noting the exact location of the needles, recoiling the spring behind the speedometer so that it rest against the pin, and clean the inside of the lens cover (the cover will scratch easily so watch what material you use to clean and wipe the lens with). If you have any burnt out instrument gauge light how would be a good time to replace them before you reinstall the instrument cluster back in the car.