DC motor problems.

I am new to this electricity stuff. I need someone to tell me why a little 3V DC motor will run perfectly off of 2 9V batteries, but with a 9V AC/DC adapter, I have to get a spark from the wire to get the motor to start.... Also if I were to get 12VDC motor with a no-load current of 700mA, what kind of adapter would I need, I don't plan on using batteries. Can't the DC motor just draw whatever current it needs? I'm using the 12VDC motor for a 7in in diameter plastic fan.

A 3V motor is normally best not overrun grossly, which is what happens with the 9V adapter. It may
burn out and the bearings wear out.

The 9V batteries cannot power motors, they are simply grossly overloaded by the motor and dropping
down to a few volts, so happen to run the 3V motor rarely normally until they die - they will also get
hot and show way below their expected capacity in mAh or Wh.

You need a 12V supply for 12V battery than can handle the stall current, or which can handle the temporary
current overload if they are not spec'd for the stall current. Steady motor current depends on load (torque), and
starting from stationary also demands more current (stall current is when the motor is not turning).

Right, xy-problem: you appear to be making a 12V fan. You can buy those, cheaply, of much better
quality than you could make yourself.

But perhaps you are making something else? And perhaps a DC motor isn't the right solution for that
either? But you haven't told us what you are trying to do, so we won't be able to help you choose wisely...

I'm just wondering about why a 9V 1A AC/DC adapter won't run my 3V DC motor. When I put five 9V batteries in a series and hooked them up to the little 3VDC motor, the motor worked could handle the voltage. The motor should be able to run off of any voltage as long as it can draw the right amount of current that it needs. 1A should surely be enough to draw from.

DC motor theory - motor speed is proportional to voltage. So, if 5 x 9V batteries in series produces 45Volts, theoretically your motor should be running at 15 times its rated speed. But as has already been stated 9Volts batteries are useless for motor running. If you mean 5 batteries in parallel to produce 9Volts at somewhat higher Ah capacity they will still be pretty useless for motor operation and will endeavour to drive the motor at 3 times rated speed.

How do I measure the amps that the motor will need to draw? Would you suggest a 12V car battery for tests on a 12VDC motor?

The easy way to estimate the stall current for a brushed motor is to measure the resistance of the motor windings. Measure across the motor power wires. With that information and the rated voltage of the motor, Ohm's law will give the estmated stall current. Stall current = rated voltage / winding resistance.