“Quote” is a verb, used as in “I like to quote Shakespeare” – in other words, when the speaker is making a reference to the person who made the original statement.
“Quotation” is a noun, used as in “Here is a quotation from Shakespeare.” As a noun, it can also be used within a statement to outline the estimated cost for something (e.g. a service or a job) as in “Our quotation for the job is as follows.”
Nowadays, you often see quote used incorrectly in adverts when someone is trying to sell a product – for example, “We can give you a competitive insurance quote” or “Contact us for an instant quote.”
Remember it this way: you quote a quotation.