This is such a wonderful question because the possessive nature of family names seems to be commonly misconstructed in various signage displays.
In this example, we are assuming that the last name of the family is Smith and more than one person with the last name Smith want to welcome guests to their home with a sign outdoors. We need to first make the name plural by adding an -s ending to the last name: Smiths. The Smith family owns that home; therefore, the sign needs to reflect their possession of it. We indicate possession with an apostrophe, so that needs to be reflected in this construction. In this example, we understand the implied nature of the word "home": Welcome to the Smiths' (home). When we remove the word "home," we are left with the proper construction: Welcome to the Smiths'.
A similar issue that arises with family names and which necessitates a different construction centers around Christmas (and other celebratory) cards. You will often see that someone has signed your card with something like "With love from the Watson's." In this case, they aren't really intending to send you love from the home itself but from the people who live inside that home. Because the meaning here is different (there is no possession), there wouldn't be an apostrophe: With love from the Watsons. This simply means that multiple people with the last name Watson are sending you love.
In short, if meaning indicates more than one person and no possession, you do not need to use an apostrophe. But if the...
family is demonstrating ownership of something, like a house in the example you have provided, youdo need an apostrophe.
One more note: if the last name ends in s, ch, sh, z, or x, you will need to add an -es to the last name before adding the apostrophe for the sign.
- Welcome to the Mattoxes'! (Welcome to the Mattoxes' home!)
- Welcome to the Jameses'! (Welcome to the Jameses' home!)
- Welcome to the Nashes'! (Welcome to the Nashes' home!)