There are many online resources which provide information on how to mount a cartridge. Generally speaking, there is usually a common set of parameters to establish installation of the cartridge based off the type of tonearm, turntable, etc.
https://youtu.be/N91uanxH-9k?si=tyXxTXzaOd4GYdds
https://youtu.be/Kr4Adsc0gFA?si=u3sD-mMf4aeHQSIu
https://youtu.be/o-iiixTiyDA?si=BPRvElm-_Anq5MWz
https://youtu.be/VDIn3fctZdA?si=gCDlP38_zBe4uep2
Watch a few of these videos and you will get the general idea.
i always have small clamp spotlight, larger mirror, tape to secure platter from rotating, needle nose tweezers, micro screwdriver set, and make sure the tonearm is secured to the arm cradle. You will get used to it after a few installations and removals of cartridges on various arms. You will end up with a cartridge setup bag, LOL. I get asked to help people setup cartridges sporadically.
When placing the cartridge leads from arm to cartridge, I use this method, I leave the cartridge slightly loose, but affixed, so that I can move the cartridge around when I need to in order to allow me to use the needle nose tweezers to slide the tonearm lead wires to the cartridge. Not loose loose, but loose enough for me to have to apply pressure to the cartridge to move it. The leads are almost always going to be a bundle of wires. Start with the most difficult wires which are harder to access, then do the easier wire leads. If you do the easy wires first, the ones that are behind or above the easy wires, they might be in the way as you try to connect the wires. This has worked for me and through experience this is what I have learned to be effective for me. This bundle of wires, may sit below the tip of the needle when all connected, make sure you pay attention the bundle of leads as you connect them to address the wire dropping or being pushed down below the needle tip as this means your cartridge rides on the wire bundle and not needle when you drop the arm down to the record. Make sure your tonearm is setup correctly first. As there are many different tonearms, I just found one installation video for a SME 309 arm, which provides some information about tonearm installation
https://youtu.be/bpLvInjGUt4?si=QP8m-aCEpfobM-_4
Another good tool is an accurate tracking force measurement device such as Clearaudio or device which gives you the ability to measure tracking force.
Lastly, do not wear long sleeve shirt, jewelry, or clothes that can snag anything. I would recommend wearing shorts and a tshirt. I would also wear tennis shoes to prevent static from happening.