You lie yourself and you lay something - the very basic thing.
You lie down on the floor OVER
You lay a pot on the floor.
This is about the present tense.
I could not find anything better than simply putting GrammarGirl's excellent examples here, in-situ.
The past tense of lie is lay, so...
Last week, Steve lay down on the floor.
The cat lay in the mud after it rained yesterday.
The past tense of lay is laid, so
Last week, I laid the TPS report on your desk.
Mary forcefully laid her ring on the table.
The past participle of lie is lain (this is wonderful), so
Steve has lain on the floor for days.
The cat has lain in the mud for hours.
The past participle of lay is laid, so
I have laid the TPS report on your desk.
Mary has forcefully laid her ring on the table.