Laid always takes an object

 
When it is used as a verb, "laid" always takes an object. Something is laid. The verb suggests an action of placing or putting something.
 
Here are some annotated examples of sentences using "laid" correctly. In each case the verb and object are colored to make them stand out.

1. "Laid" as an active verb with an object

I laid my hand on her arm.

Before he lay down for his nap, he laid down the law about children disturbing his nap.

He triumphantly laid down his cards--four aces.

Newton's Theorem provided a method for finding the sum of the nth powers of the roots of an equation and laid the foundation for the theory of symmetrical functions of the roots of an equation.

Every day I plucked a nosegay of my finest flowers, and when it was dark in the evening, I climbed over the wall and laid it upon the lady's marble table.

My ball python just laid seven eggs.

The Pope laid plans for a visit to the Holy Land.

A simple job turned into a household comedy when her husband laid the carpet on the stairs.

2. "Laid" as a passive verb with an object

The passive voice, as you remember, contains some form of "to be." In passive sentences, the object of the active verb appears as the subject of the sentence.

Active: The boy hit the ball.

Passive: The ball was hit by the boy.

The sale of Fermec was one of the conditions laid down by the European Commission when it approved the merger of Case and New Holland.

Compare this paraphrase of the previous sentence to put it in the active voice:

When it approved the sale of Fermac, the European Commission laid down the condition that Case and New Holland must merge.

The rules for deciding who can have financial help from Social Services and how much financial help they get are laid down by central government, and are the same all over the country.

There are statutory requirements for certain documents to be laid before the Assembly.

The first three of the Kursk victims were laid to rest yesterday.