Measuring Tensile strength [How do you do it at home ?]

My first thought is, thats funny, but heres goes. Youre probably better off figuring out what your metal is approximately, and then looking up the properties. Mechanical testing, by a novice, with only one ingot, using a makeshift setup is going to give you junk for results, but you can always try. Tensile strength is not too challenging as long as you can prepare a decent specimen. At the very minimum some sort of hydraulic press, that you could rig to stretch a sample, with a pressure gauge would be essential and additionally the ability measure elongation would give you strain to failure & % elongation ( a simple micrometer/caliper would work). You would have to have the ability to attach the specimens in some kind of secure jaw and prepare a nice neck to make sure you sample breaks where you want. You will need a micrometer to measure the fracture surface area to determine your stress to failure (load / area) and then you are set. See what you can get with tensile strength, dont bother with the shear yet.

Here is an example of a typicaly tensile testing setup using sample dogbones.

It would be really difficult. You would have to make a homemade tensile tester with a pressure gauge. You could you a gear system attached to a screw bolt.