I have an Amana central ac unit and the fan motor won't shut off, just replaced and installed new motor, thermostat on auto, switch to off and still doesn't stop running?

You cold disconnect the fan wire on the thermostat(maybe green?)and if it stops, problem is at the Thermostat. If Not, a short on the control wiring.
The Fan May have a Delay, could be several seconds, after disconnecting the Green?

You cold disconnect the fan wire on the thermostat(maybe green?)and if it stops, problem is at the Thermostat. If Not, a short on the control wiring.
The Fan May have a Delay, could be several seconds, after disconnecting the Green?

Where is the control wiring located?

You have 1 set of control wiring that goes from the thermostat to the Air Handler, and another set of control wires for the outside compressor, it also goes to the Air Handler.
Good Luck
If you disconnect the green(if blower) at the thermostat and it keeps running, then you disconnect the green in the air handler and the blower stops, the red and green? Are shorted between the thermostat and air handler.

You have a fan relay that may be stuck. The green wire from the thermostat hooks to one side of the coil on the fan relay and the other side of the coil goes to common on the low voltage thermostat. To test it turn off the power and use an ohm meter to read between "R" (red) and "G" (green) (most of the time installers keep to this color code) with the green wire disconnected at unit. If it reads zero or right at zero ohms then this circuit is closed or you have a short. If it reads infinity then the problem is the fan relay. The fan relay has a 24 volt coil on most units in homes. Sometimes you will have a relay that has two sets of contacts and only one is used. If that is the case you can sometimes tap on it with a screwdriver to unstick the contacts and just move over the wires to the other set and it's fixed. There are three terminals: (1) power coming in, (2) in the middle a normally closed set of contacts with this symbol: ≠, and (3) the normally open set with this symbol: = with a line on the top and bottom of each symbol. The normally closed set goes to low speed (red) on fan and can go through the fan control for heat first or straight to the red or blue fan wire. The normally open set goes to the high speed fan wire which is black, but sometimes it's wired to blue, or medium. If at any time these wires are shorted it will immediately burn up the fan motor. Don't do it, or wire it wrong. I hope when you replaced the fan motor you added a little oil in oil holes and cleared them of trash. This is one of the easiest fixes you can do. If you have a single-pole fan relay just buy another one and make sure to buy the highest amperage one you can get. About 20-30 amps inrush will be best to keep the problem from reoccurring.

You have 1 set of control wiring that goes from the thermostat to the Air Handler, and another set of control wires for the outside compressor, it also goes to the Air Handler.
Good Luck
If you disconnect the green(if blower) at the thermostat and it keeps running, then you disconnect the green in the air handler and the blower stops, the red and green? are shorted between the thermostat and air handler.

Also wondered if the blower is supposed to blow out the top of ac away from motor or blow/suck inward toward motor-Does it matter clockwise or counterclockwise the direction of the fan rotation?

It absolutely matters! The fan turns the way the fan blades face on this type of blower called a forward-curve blower. Looking at the side of the blower if the blades are like this:/// then it turns toward right and vice versa if they look like this: \\\. Another way to tell is to look at it from the end away from motor and if the outlet is on left top then it's clockwise (///) and on right it's counter-clockwise (\\\). It's very important for the blades to be clean because just 1/16" of dirt in cups of the blades will cause a 33% loss of airflow. The speed must be right, too. There are usually arrows pointing in the right rotation. Make sure to check and clean the coils with a good foaming alkali coil cleaner. Nothing kills efficiency like dirty coils. Use a good pleated filter on your unit.

It absolutely matters! The fan turns the way the fan blades face on this type of blower called a forward-curve blower. Looking at the side of the blower if the blades are like this:/// then it turns toward right and vice versa if they look like this: \\\. Another way to tell is to look at it from the end away from motor and if the outlet is on left top then it's clockwise (///) and on right it's counter-clockwise (\\\). It's very important for the blades to be clean because just 1/16" of dirt in cups of the blades will cause a 33% loss of airflow. The speed must be right, too. There are usually arrows pointing in the right rotation. Make sure to check and clean the coils with a good foaming alkali coil cleaner. Nothing kills efficiency like dirty coils. Use a good pleated filter on your unit.

Thank you for the info- Would you know if there's a way to get a manual and wiring diagrams for my ac unit or even find it online somewhere to print it out?

Look at these: https://dl.dropboxusercontent.com/u/8010163/AC%20Wiring%20Diagrams.zip
Wiring diagrams for AC units are very generic: they are almost all alike. You have a fan relay and sometimes a heat strip relay in the inside unit and a compressor contactor on the outside, unless it's a heat pump where you have a defrost board and reversing valve. It's all very simple. You just cannot fix anything without having a meter and understanding it and the wiring.

Don't let it get complicated on you.
Find the contactor/relay for the Blower, see if when 24 volts is present, the contacts close, and when removed, the contacts open and shut off fan. The meter will tell if contacts are welded/fused closed.
You will also find out if thermostat releases the blower control wire(green?)

It is very simple.

Follow the wires back from the Blower Motor, you're getting close.
Even with breaker off, treat Blower as if it could go on at any time, to be safe.