modular arithmetic - How to calculate a Modulo?

I really can't get my head around this "modulo" thing.

Can someone show me a general step-by-step procedure on how I would be able to find out the 5 modulo 10, or 10 modulo 5.

Also, what does this mean: 1/17 = 113 modulo 120 ?

Because when I calculate(using a calculator) 113 modulo 120, the result is 113. But what is the 1/17 standing for then?

THANK YOU!