Lie and lay are easy to mix up because their forms overlap.
Use lie when no direct object follows. It means recline, rest, or be in a flat position. Use lay when something is being placed somewhere, so it usually takes an object.
- Present: I lie down every afternoon. I lay the keys on the table.
- Past: Yesterday I lay down after lunch. I laid the keys on the table.
- Past participle: I have lain there for an hour. I have laid the keys there before.
A quick test can help. If you can ask lay what? and answer it, lay is probably right: She laid the blanket on the grass. If there is no object, lie is probably right: She lay on the grass.
The biggest trap is the past tense. The past of lie is lay, which is why sentences like I lay down for a nap are correct.