Answer:
Plural
If referring to something about the Smith family as two or more, it would be the plural Smiths. Ex. The Smiths have two daughters, one son, a dog, a parrot, a hamster, and one snake.
*In the above sentence "The Smiths" takes the place in the sentence for "The parents".
In addressing, say a Christmas Card, it would be The Smiths.
Possessive
If referring to something owned by a person with the last name of Smith, it would be Smith's.
Example sentences of possession:
The Smith's dog chased our cat up a tree.
The noise that kept me awake until 2 a.m. was the Smith's dog.
When the Smiths held their New Year's Eve party, one of the Smith's cars and one of the Jone's cars collided in the driveway. (bold is plural, the other two are possessive)
Johnny is one of the Smiths living on Second Street.
A roofer discovered that raccoons were living in the Smith's attics and promptly told the Smiths about the various health and safety risks associated with removing the animals. bold is plural, the other is possessive)