Furnace High Pitched Squeal
If the blower in the furnace is belt driven (not likely), the belt might be worn and slipping. Most likely, the blower is direct drive, which means you'll probably have to pull out the entire blower assembly to get at the motor.

WARNING: 


Before removing the blower, make sure power to the unit is OFF. 
If you have to remove wiring to pull out the blower assembly, make sure you label each wire so you know where it goes.  


Once you have the blower out and accessible, you should be able to locate the two oil ports. These ports are typically on the "top" of the motor, and are plugged with plastic or metal caps. Remove the caps, fill it up with oil, and replace the caps. Check the manufacturer's documentation for the type, and amount of oil to use.

Here's a good YouTube video from Grayfurnaceman that shows How to oil the HVAC fan motor.

If the motor in your unit does not have oil ports, you might have to replace the bearings, motor, or the entire blower assembly (depending on which unit you have).

As always, if you don't feel comfortable doing this type of work, please contact a local licensed HVAC technician.