Buttons and motors

Ugh, starting out on arduino, I thought the basics would be easy, but i'm struggling right off the bat, ok so I have a 3-12v dc motor, and a 9v battery. So here's what I got so far:

Plug positive of 9v to one motor lead, plug ground of 9v battery to motor; motor spins; yay baby steps!

Wire momentary push button lead1 to positive 9v lead, wire push button lead2 to motor lead1, wire 9v ground to motor lead2; motor spins when button is pushed; weird to see cuz I would think motor would need a ground to the pushbutton instead of just to 9v but I physically see the circuit so I'll take it!

Now I have an arduino, now I need to wire this set up to the arduino to program this button...and i'm lost...

Unplug 9v ground from motorlead2 and plug it into arduino gnd? Then run jumper from some arduino pin to motorlead2 for ground? That would connect the arduino to the circuit, but I still need a pwm pin jumped to the pushbutton right?...my brain hurts...

You can't use Arduino to control the motor directly - the 9V will break the '328P chip.
You need to a use a transistor, wired up like so:

Thank you for taking the time for that response, so I see on pin9 the resistor going to the transistor to the motor with the diode to prevent the reverse current to the 9v. I am not sure how to read the arrows that connect each other. The gnd pin on the arduino goes to ur blue arrow...is that going to 9v ground? And then d2 is just the pushbutton that is then then connected to the transistor...

Sidenote, i'm still grasping the math behind resistors, how do a I calculate the resistor ohms for the 9v and then a future 12v power supply...

The diode prevents the inductive load from destroying the semiconductors by allowing
a path for current on switch-off. You always have to consider this when switching
inductive loads like relays, motors, solenoids.

Resistors relate voltage to current. Here we use 150ohms or so to limit the Arduino
pin output current to a value within its limits (abs max = 40mA). The resistor is nothing
to do with the motor supply, it goes between the Arduino pin (5V) and the transistor base
(0.7V). The base-emitter voltage is about 0.6 to to 0.8V typically.

Not shown on that diagram is that the internal pull-up resistor is enabled for the button input
pin.

Grounds are commoned.

Learn the standard symbols for ground, supply, transistors etc by heart ASAP,
it will help a lot.