How to wire a 3 prong dryer cord
First, remove the cover that protects the dryer terminal block. The dryer terminal block will have 3 lugs with nuts, Phillips or slotted screws. Connect the left and right wires from the cord to the left and right posts of the terminal block. The left and right wires from the cord can go on either side of the terminal block they are interchangeable. However it is very important that you connect the center wire from the cord to the center post of the terminal block.

How to wire a 3 prong dryer plug
How dryers work | How electrical dryers work
Electric dryers in the US operate on two 110-volt A/C circuits. The two 110-volt circuits combine to deliver 220 volts A/C to the dryer heater. The dryer motor operates on 110-volts A/C. Dryer receptacles have an L-shaped neutral post. 4-post receptacles have the L-shaped neutral and a separate ground. 4-post receptacles require 4-wire cords to isolate the neutral from the dryer frame.
You can check the voltage to your dryer by slightly sliding the cord out of the receptacle and using the leads from a multimeter to check for voltage on the blades of the cord that slide into the receptacle. Between the left and the right blades you should read 220 volts. Between the left or right blade to the center blade (the L-shaped blade) you should read 110 volts AC.
Technicians check for voltage when the dryer is attempting to start or not heating for a very specific reason. Checking for voltage without the dryer plugged in does not tell the full story. A dryer heater uses 220 Volts and draws about 20 amps when it is heating. Checking for voltage from L1 to L 2 on a defective circuit may show 220 volts but when the heater kicks in and starts to draw 20 amps the voltage may drop off to 0 volts. Imagine the wiring to your dryer was stranded wire. Stranded wire is composed of a number of small-gauge wires bundled together to make a larger wire. What if all but one of those stands were cut and only one small wire was completing the circuit? Reading voltage at the receptacle without the dryer plugged in you would read 220 volts from L 1 to L 2. However with the dryer plugged in and the heater attempting to draw a heavy current, the electrons (current flow) would be dammed up behind the cut and only a small amount of current would pass through the wire. Certainly not enough to make the heater heat. There are a lot of things that can cause a partial circuit but the result is the same as the stranded wire example.