Check the density of the coin
Compare to expected density of silver (10.49 g/cm^3)
Profit

The easiest way to do this is to have or fashion a scale which can measure tenths of a gram or better.
Yes, you can make a DIY balance scale with common household items which can measure those tiny amounts.

Next you need a plan. Your mission is to compare the mass of your coin to the mass of an equal volume of water. The most common way to do this for objects that sink is to
1) find 2 containers which hold water
2) fill one of the containers and position it such that if you add anything at all to the full cup, it will overflow into the other cup.
3) Measure the mass of the empty cup or put it on the scale and TARE the scale (zero it).
4) GENTLY place your coin into the full cup, so that it spills its volume's worth of water into your empty cup.
5) Measure mass of displaced water. If you didn't TARE the scale, then take this final measurement minus the initial measurement to find the change in mass due to the displaced water. If you did TARE the scale, then it's reading this amount directly.
6) Retrieve your coin, thoroughly dry it off and measure its mass. (Prob should have done this first, TBH, sigh)

Since the density of water is 1 g/cm^3, then simply dividing the mass of the coin by the mass of the displaced water is your goal.

If it's very close to 10.49, then prob silver or at least worth checking further.


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However... Unless you have a beautiful, perfect, sharp relief coin which has NEVER been in the sun or in a pocket or had any thermal or mechanical stresses applied to it, then don't expect to get much more than the 2p of value from it. Coin collectors are the most tedious perfectionists in the world. If it's not just a mint coin, but an exceptionally perfect mint coin, they're not going to shell out big monies for it.