How to calculate current drawn by microchips, transistors and diodes?
As you move up the food chain from passive devices to active ones (LEDs, transistors, etc.), power calculations vary from a little bit more complex (LEDs) to very complex (multi-core microprocessors).  Start with the simple step, LEDs.  Learn what the forward voltage is and how it affects the most basic circuit (battery, resistor, LED) calculations.
Electronics is no different than any other complex discipline - the hard parts are built up on many layers of increasingly complex ideas and concepts.  Start small, draw a basic schematic, try to figure it out, then post the schematic and your questions.