Controlling LEDs is pretty straightforward.
Its just a fancy diode, yes?
So you apply a higher voltage to the anode, a lower voltage to cathode. If the difference is big enough (~1.8-2V for a Red LED, and up to ~3.2-3.6V for a green or blue LED, shown as Vforward onthe datasheets), the diode will conduct current and light up.
When it turns on, it will pass all the current the 'supply' (be it direct connection to a regulator, or from the pin of an IC), and burn up if the current is not limited.
That is usually done by means of a current limit resistor.
This is where ohms law comes in.
The Voltage from the supply is dissipated across the resistor and the LED.
So you have a 5V supply, a Vforward of 2V, and you want to limit the current to 20mA to keep the LED from burning up, you do a little math.
Voltage (V) = Current (I) x Resistance (R), or V=IR. Re-arrange a little: V/I = R, voltage/current = resistance
You know the voltage across the LED, the remaining voltage is dissipated by the resistor.
So (Vsource - Vforward) is the voltage across the resistor. You know the current you want. Solve for resistance.
(Vs - Vf)/I = R
(5V-2V)/0.02A = R = 150 ohm.
Everything after this assumes you will have a current limit resistor.
The LED doesn't care how that Vf is created. You can have the source be the power supply to cathode, and an IC (which is just transistors) pin going low to make the cathode low.
You can have an IC making the anode go high, with the cathode connected to ground.
You can have both - an IC/transistor making the anode go high, and another IC/transistor making the cathode go low - that is the heart of multiplexing, by the way.
If you have a bunch of LEDs you want to turn all at once, they can be connected in parallel (with a resistor each) and a lower voltage level used to power all of them.
If you have a higher voltage level available, the LEDs can be connected in series with just a single current limit resistor.
Say 12V was available, and you had four 2V LEDs, then (12V - 2V -2V -2V -2V)/0.02A = 200 ohm.
efficiency? - often it is more a matter of convenience.
A single transistor is all that is needed to control current flow thru LED.
However, if you're trying to control 8 LEDs, than 8 transistors all bundled up nice & neat in a 16 pin IC is a lot more convenient to deal with. 8 input pins, 8 output pins, common ground pin, and 8 current limit resistors. Vs 8 resistors to control the base pin of the transistor, 8 collector pins connected to 8 current limit resistors, 8 emitter pins connected to ground. You can see how the space & parts build up pretty quick.
Clear as mud now?