First, make sure that the microphone is not broken or damaged. Test it on another PC and see if it works. If it works there, then you can just do some things on your PC.
You can eventually test a different microphone on your PC, see if that one works or not.
There should be an option there, an item called “Microphone” and it should look active (not gray).
If it is gray, then it means that you need to install new audio drivers, the ones that you have right now are not that good, even though the sound might work on your computer. That item called “microphone” should always be active, no matter if a microphone is connected to your computer by USB or normal jack connector.
After you install the right audio drivers, the microphone should work with no issue. Test it on Skype.
Also make sure that the microphone jack is inserted into the correct port, usually it is pink-orange.
The green port is for speakers or headphones.
To get the correct audio drivers, you can download the software CPUz that will detect the name of your motherboard. Then search on google “motherboard name audio drivers”.