Where would I get the resistance or current when I am setting up a few LEDs for example?
You decide on what current you want. You do this from the data sheet and how bright you want them. Most small LEDs take 20mA maximum but they are nearly as bright with only 10mA.
Having chosen the current you calculate the resistance.
The LED will have a forward voltage drop depending mainly on the colour. Say it is red then it would be about 1.8V BUT see the data sheet for your LED for the exact value. Subtract this from your 5V supply, so you get the voltage across the resistor:-
5 - 1.8 = 3.2V
So to get the resistor that will have 3.2 Volts across it when there is 10mA through it use ohms law:-
R = E/I ...... = 3.2 / 0.01 = 320 R ( or ohms )
Which is close to what you have been doing.
From an arduino pin too many amps is 40mA, keep it below 30mA.