Friedrich Mohs, a German mineralogist, developed a hardness scale in 1812. This was created to assist with the identification of minerals and ranges 1 being the softest (Talc) to 10 being the hardest (Diamond).
The scale is as follows:
Here's a great resource for you to learn more about testing for hardness.
Some minerals are magnetic such as Magnetite. See if your mystery mineral is magnetic by placing a magnet next to it.
Some minerals contain carbon and oxygen and will have a fizzing action when vinegar or HCL is applied. HCL is hydrochloric acid. and should be handled with care. If you do not have HCL, then try vinegar. I recommend trying vinegar first anyway. Drop one or two drops of vinegar onto your mystery mineral and look for any fizzing reaction. Please note that the vinegar is a mild acid and the fizz action isn't as prominent as it would be with HCL. I use a magnifying glass and good lighting to look for the fizzing. It's also important to note that this test works best with a rough speciman. If there is no fizz, then try HCL. Any fizzing action will tell you that your mineral is a carbonate. I use this test ot help identify Calcite. Other possibilities include: Aragonite, Dolomite, Azurite, Magnesite, Rhodocrosite and others.
Other Things to Consider
Most crystal folks really have no interest in mineral identification techniques. I totally understand that! But it is important to have some knowledge, especially when purchasing crystals and minerals. A great tip is to research. Look up: How to identify......(and fill in the blank). For example, "How to identify Jade". You will find wonderful articles with tips. A great resource for the physical characteristics of crystals and minerals (hardness, streak, chemical composition, etc.) is