Buying nearly any appliance part will require a model #. Since all appliance parts are given a designated part #, this # must match the model it is suited for. Since most user manuals contain information on several models, it is important to get the model # directly from the appliance model tag. The first 2 digits of the serial # may also be needed for some parts as well, so always get that too. With this information, you can contact any parts house or research the web to find a part #. Be aware that some websites do not use the actual part #, but a private stock #. They do this to discourage price shopping, hoping to get rewarded for helping you find a needed part.
Finding your model tag depends on the appliance. See this FAQ page for some pointers:
Hope this helps!