How can I find out a components voltage rating and amperage draw?
You are right, measuring a components characteristics has some error, and at best only tells you what that one component at that time and that temperature can do.  What you really need to know to design circuits with components is the maximum range of various parameters.

This is why each component should have a accompanying document called a data sheet.  The manufacturer of the component creates the datas sheet, and usually makes it available on their web page.

There is no substitute for using the datasheet values in proper circuit design.

For one-off or hobby purposes, you can take a few guesses with parts that are similar across manufacturers.  For example, 0805 resistors can usually dissipate about &frac18; W.  If you have a bunch of unknown 0805 resistors, you should be quite safe keeping their dissipation to 100 mW and the voltage across them to 50 V.

Just about every LED can handle 20 mA.  Modern LEDs are efficient enough that 10 mA is usually plenty for indicator use.  That really should be OK with pretty much any LED you're going to find.  LED voltage is also a function of the color, due to physics.  Common "green" LEDs usually drop about 2.1 V, for example, red ones around 1.6 V, IR about 1.2, etc.

The power dissipation of a component is largely a function of its package and geometry.  You can therefore take reasonable guesses about the dissipation capability of simple components in common packages by looking at datasheets of those similar components.  Still, that's no guarantee, and would be irresponsible engineering if done professionally or for a production product.

More complex parts are more unique, and there is less you can infer from similar parts from other manufacturers.

Go back to whoever you bought the parts you have from and ask for the data sheets.  If a component is marked with a manufacturer and part number, then go to that manufacturer web site and look up the datasheet.