Controlling different leds over serial

Im using 100 ohm resistors right now.

A bit low but should be ok.

You need to add code to drive those.

Then I'll figure out how to expand the circuit from that with more leds

Fine that is a project in itself with diffrent ways to go however you might want to look at this:-
ShiftPWM library
http://www.elcojacobs.com/shiftpwm/

How can I draw out my circuit with the arduino and breadboard like in the tutorial?

fritzing.org/

But please post a real schematic.