How does current split in a circuit?
I'm not sure what exactly you are asking but basically:


If the component says it needs a certain voltage, you need to give it that voltage. 
If it says it's maximum current draw is x Amps, you need a supply that is capable of providing at least this or more. The chip will only pull what it "needs", so it doesn't matter (in 99% of cases - if it does matter, the datasheet will make this clear) whether your supply is capable of providing 1000 times the current required.
If you have multiple ICs that need different voltages, you need multiple rails - there isn't a way round this. With multiple ICs on one rail, add up their maximum current requirements and make sure your rail can handle more than this. So if all your ICs run at 3.3V, then you can use one 3.3V rail capable of providing the current of all the ICs added together. 
There are situations where even though the ICs run at the same voltage, you may wish to use different rails (of the same voltage) for them. An example is a sensitive analogue circuit on one area of your board, and a high speed digital circuit in another area of your board. It's generally a good idea to use two separate regulators and rails in a case such as this.  
If you are using a linear regulator, make sure you calculate it's power dissipation. For a large voltage difference between IN and OUT combined with a reasonable current draw, it's often a better idea to use a switching regulator.
For example 12V to 3.3V at 500mA will waste around (12V - 3.3V) * 500mA = 4.35W of power which will be disspated as heat in the regulator. The thermal specifications will tell you how hot the regulator will get without a heatsink. For example, if the junction to ambient (&theta;ja) spec is 50&deg;C/W, then the temperature will rise to 4.35 * 50 = 217&deg;C above ambient (so obviously you would need a heatsink in this scenario, most silicon devices have a max operating temperature of ~125&deg;C )

So in summary, read the datasheet thoroughly for each component, check it's voltage and current requirements and tolerances (i.e. how much it can be over or under the nominal value) and make sure your rails are capable of meeting the specs. There will often be advice on layout and a basic circuit shown in the datasheet.