What would happen if another substance competed for the enzyme active site?

That's what is called competitive enzymatic regulation. If there are more of that substance than the enzyme substrate, then most of the enzyme, if not all depending on the substance's concentration, will be inhibited on its action. If there are more substrate then the competitive substance, the expected reaction for that enzyme will happen at an expected rate. If the ratio substrate:substance is 1:1 then the reaction enzyme-substrate is very slowed down.