I understand connecting motor voltage directly to esp8266 can cause problems, but I shouldn't need 2 power sources. how does my desk fan only have 1 plug, but all the wiring diagrams show exterior motor voltage supply?
Please post your own, correct, hand drawn circuit diagram, rather than someone else's.
I shouldn't need 2 power sources.
Perhaps, if you have studied and understand intermediate electrical system design concepts, and learned how to remove the nasty noise spikes and Arduino-resetting voltage drops that motors introduce into the power leads. Useful search term: "power supply decoupling".
Until then you are far better off powering motors and Arduinos separately, but don't forget to connect the grounds.
Post an annotated schematic, by the time you have it drawn you will have an idea of how the circuit works. Also obtain a copy of the Arduino Cookbook and you will find the bulk of your project in there.
After some research I found a voltage regulator is great for filtering power from various supplies before circuit components. I'm assuming because the added capacitors store the extra energy to level out any dips?
so then can I just add 2 to my circuit below to handle any problems? or is the problem between the esp signal and the driver?
You need to filter the power to the MCU, not the motor.
The motor power supply should be chosen to handle at least twice the maximum expected motor current (e.g. for a brushed DC motor, the start/stall current).
Forget my schematic drawing. The question is, is putting a voltage regulator the same thing as you said previously about filtering the power to the mcu.
I did not intend for this thread to be specific to an exact schematic. It's supposed to just be talking about the generality of powering a circuit board and a motor off the same plug.