Making 10mH inductor on my own
Any piece of wire has an inductance, we increase the inductance by wrapping many turns of the wire into a coil on a former. The inductance of the resulting coil will be affected by the number of turns, the diameter of the coil, the length of the coil, the shape of the coil and the material it is wrapped around.

You can find many on-line calculators that will give you the inductance of simple cylindrical air cored inductors. And a few that will give you inductance of more complex arrangements eg: http://coil32.net/

To make your own, you need to have enough wire to make the coil, - the wire must be capable of carrying the current you need it to take, and a former to wind it on.

But as @RogerRowland says, there are plenty of 10mH inductors available out there, and lots of designs for metal detectors, that include the design of the search coil.