I have a battery amperage tester. Should I just hook up the cables between that and the battery? Or something else.

If you havr an amp tester, add it to a test battery and take it away and see if there is any difference.  Check clamp connectors for frays, redo the clamp if its bad.

Shiny bright copper, good. Crusty green copper, bad.

Just like battery cables. The more strands and bigger, the better.

Best cables are LONNNNG cables, you can't always get to the front of the other vehicle. Front bumpers aren't conductive anymore, a coat hanger wont do it.

Rule #1 about jumper cables is never loan them out, loan yourself out, with the cables. You always get them back that way. Rule #2 about cables is that if you have to use them, enough wasn't done to prevent it. It's always the owner's fault his system went tits up. Fix the problem in the head and their won't be a problem under the hood.

Rule #3 is always observe #1 and #2, you will only buy one set and use them one time for yourself. They will quietly sit in a dry protected place in the car until you meet someone who doesn't know #1 and #2, at which point they will see a working example of why they should.

Really, there should never be a reason to have some, but, being human, we don't follow logic or common sense much. And cables are proof.

Easiest way is to visually inspect for corrosion or rust. Another way (harder) would be to test for voltage drop. That would require a load though to accurately test for that which is the harder part.

For example, connect a battery using the cables to a starter (think bench test). You would then measure the voltage at the battery then at the other end of the cable at the starter and note the difference. Then you would have to know what a normal voltage drop for that particular starter is and compair.

The voltage drop test would be the most accurate and it dont lie but requires a load in proportion to the cable/wire tested.

To make this more accurate, you need a Wheatstone Bridge.  There are micro-ohm meters that have calibrated bridges inside that can measure the small resistance of the cables.  But, these things are out of the budget for most folks.  

Rule #87: Get the best, biggest, and longest you can afford. I’ve got four or five fairly expensive sets. One set out performs others by a mile. I jump off tractors, trucks, lawn mowers, and other stuff all the time.

Yup, totally my fault the GM "Mark of Excellence"/UAW assholes at assembly of my first car sandwiched a hot wire for the power door locks between the firewall and the plate at the bottom of the steering column, causing a parasitic draw and killing the battery.  

Owner error on battery maintenance, for sure!  

Yup what he said.

I have a set from when I was in the Army that is 25" long and made from heavy welding cable. It held up to jumping the heavy duty 24volt systems on military vehicles so 12volts doesn't phase it. I don't let that jumper cable out of my sight ever!

Are you an electrical engineer? That is getting very deep into it.