Use there is when the noun that follows is singular, and there are when it is plural.
Examples.
There is a cat on the rug.
There are two cats on the rug.
There are a dog and a cat on the rug.
There is may be contracted to there’s, especially in speech. There’s is also often used before a plural noun in speech and informal writing.
Example.
Informal: There’s a dog and a cat on the rug. Formal: There are a dog and a cat on the rug.
