I have a Dayton 2m145 universal motor that has four wires as shown in attached image. Red connected to brush and yellow connected to other brush, purple connected to armature and grey connected to other side of the armature. I know nothing about motors, please help connecting to 115 volt wall output.
One armature (brush) wire should be connected to one field wire. The other armature wire and the other field wire should be connected to the two AC power wires. If you connect the correct armature wire to the correct field wire, the shaft should turn counter clockwise when viewed from the shaft end of the motor. That is assuming that the Grainger information in the link supplied by @replete applies. If you pick the wrong armature and field wires to connect together, the motor will run in the opposite direction, the commutator may spark a lot, and the motor may otherwise not perform very well.
Things that are taken apart with no record of how they should be put back together have a high risk of becoming worthless.