Lets vs let's

To let means to "allow".

Let him in. = Allow him to come in.

The word "let's" means "let us"

The first comes with the pronoun "us".
The second does not come with the pronoun "us".


She lets [allows] him to paint. = She allows him to paint.

So the rule is that when you mean let us, or allow us, or permits us, you use let's.

The following examples do not have the plural pronoun [us] contraction so no apostrophy is used.

She lets me paint. = She allows me to paint.
She lets them paint. = She allows them to paint.
She lets him or her paint. She allows him or her to paint.

Credit: http://www.englishforums.com/English/LetsVsLets/gnbh/post.htm from Radrook