I'm an American in Ireland, I'm going to be entering the UK and then France by land. I heard if traveling by bus or car many European borders don't have custom stops when entering. How do I get my entry and exit stamps for my schengen visa?
You will most definitely have an immigration check on exit from the UK and on entry into France. For the Eurostar train, you will do both in the UK (French officials are allowed to do this). Otherwise, your Schengen visa will be check as you enter France. [EDIT: Not correct; see comment below. Only arrival by air is checked in France; other types of transport from England will be checked at departure.]
What you have heard about is the Schengen Zone. Many European countries have abolished immigration and customs checks at their shared land borders, so going by bus/train from France to Germany, Belgium, Spain, Switzerland, will be as uneventful as going from New York to Connecticut.
[SECOND EDIT: I missed the OP’s statement that he is an American. If he truly is a USA citizen, he does not need a Schengen visa at all for a tourist or business visit.]