I need some help with finding out how to power LED's (And how "power" works in circuits in general)
A constant voltage power supply (the most common type) will deliver a fixed voltage at any current up to its rated maximum.  The actual current delivered will be determined by the load (assuming the load is designed to work from the supply's voltage).

If you have two LED strips in parallel, each requiring 5 volts at 600 mA, you would need a 5 volt power supply capable of delivering at least 1200 mA (1.2 Amp).