Pour is a verb which means “to cause to flow in a stream,” “to dispense from a container,” “to give full expression to,” or “to move with a continuous flow.” You might pour milk, or pour out your feelings, or the rain can be pouring.
Pore, when used as a verb, means “to read or study attentively.” It is usually paired with the word over. For example, you might pore over your textbook in preparation for an exam.
To remember which is which, I like to imagine that the little “u” in pour is a cup, into which I am pouring water. If there is any sort of transfer of substance or expression of emotion, then you have to have that u to pour it into.
Pore can be used as a noun, in which case it refers to the small openings in your skin through which you sweat. Poor is also pronounced like pour and pore; however, it is an adjective that means “lacking in money or some other substance.” They should be easier to keep separate, since they are different parts of speech, but watch out for them just in case.