So far, I've dealt with only devices like resistors, capacitors and inductors. Calculating the current drawn by these devices is very simply by using the formulas I read in my Physics textbook (e.g. V = IR, Q = CV etc). But how do we calculate the current in case of a connected diode, LED, transistor or a microchip. Sometimes some examples refer to a forward voltage or some direct value of current and do the calculation, which confuses me completely. How can I find out these values of voltage and currents so I can solve the circuits just like I was able to when I dealt with circuits with R, L and C (individual or in combination).
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.
Get any edition of Grey and Meyer "Analog Integrated Circuits".
Read up on "bias generators", which often use some version of "band gaps".
In ananlog/RF ICs, you'll see the "vout" of the bias_generator running all around the IC, to control the currents by using the "matched diode" assumptions. Which in an IC with internal heat generation, will not be true.