These two verbs cause a great deal of confusion, but they're really not all that tricky. To "lie" is to "recline." It's an intransitive verb, meaning it doesn't take an object. For example:
Now, I lie on the operating table, nurses bustling around me.
To "lay" is to "place" or "put." It's a transitive verb, so it needs an object. You lay something:
I walk into Hugo's room and lay the sweater on his bed.
Past tense confuses things further. The past tense of "lay" is "laid."
Last week, I walked into Hugo's room and laid the sweater on his bed.
The past tense of lie, however, is lay:
Just yesterday, I lay on the operating table, nurses bustling around me.
Yep, you read that right. The past tense of the intransitive verb is the same as the present tense of the transitive verb. No wonder people get tripped up. But now that you know, you won't. So lie back on your recliner and lay your laptop on the table. You deserve the break.