Lie Vs. Lay

"Lay her i' the earth;
And from her fair and unpolluted flesh
May violets spring!"
-- Hamlet, Act V, scene i

Why didn't Shakespeare write "lie her i' the earth"? According to Webster's, "lie" means to "be or stay at rest," while "lay" means "to put or set down." Wouldn’t Ophelia be staying at rest in the earth? Many people are confused about the difference between these two words. I still have to look up the verb tenses whenever I use them.

In the example above, “lay” is correct. The easiest way to decide whether to use “lie” or “lay” is to think about the item in question. If the noun has agency, in that it performs the action, then use “lie.” If Ophelia had still been alive, and could choose to rest upon the ground, then “lie” would have been the right word to use. A person lies on the bed, as does a dog in front of the fireplace. If, however, the noun is an object, without agency, then use “lay.” A body can’t lie itself down, but it can be laid to rest. A book can’t lie itself on a chair, but Laura can lay the book on a chair.

Confusion results from changing verb tenses. The past tense of “lie” is “lay.” (Yes, really. Don’t you just love English?) So yesterday, the dog lay in front of the fireplace. The past tense of “lay,” on the other hand, is “laid,” as in “she laid the blanket on the sofa.”

This chart shows the different tenses for lay and lie:

Here are some examples of conjugating the rest of the tenses:
The past participle of “lie” is “lain”: Faith has lain in bed all day.
The past participle of “lay” is “laid”: Dawn has laid the stamped envelope in the out-box. 
The present participle of “lie” is “lying”: The lizard is lying on the rock in the sun. 
The present particle of “lay” is “laying”: The dollar bill is laying on the ground. 

Remember, “to lay” means to put an object down. “To lie” means that the subject has agency and can recline itself or stay at rest.