Here is my first and best technique: AVOIDANCE. If you write it "The _____ family," you can put their surname unaltered where the line is and be done with it: "The Sampson family." "The James family." "The Moss family." And of course you could also write "Jim, Melanie, Caden, Olivia, and Isabella Sampson" and be done with it that way, too, but goodness, that is a lot of writing, and also sometimes I am not entirely sure I have all the first names straight.
If you choose to avoid avoidance, we will begin with the easiest: straightforward surnames such as Sampson. If you want to address the envelope to the entire household of Sampsons, it's a simple plural like cat/cats and you add S at the end: "The Sampsons."
- NOT: The Sampson's, which makes no sense.
- NOT: The Sampsons', which is a structure that would need to be followed by a word telling us what it is they are the owners of, such as a boat or a cat. You might be able to justify writing it The Sampsons' if you argued that "Residence" was implied, but I'd save that iffy excuse for if you mess it up accidentally.
Mid-level difficulty next: surnames ending in S, such as James. If you want to address the envelope to the entire household of Jameses, it's the regular plural for words ending in S, like bus/buses: you add ES, and it's "The Jameses."
- NOT: The James', which makes no sense.
- NOT: The Jameses'; see The Sampsons', above.
- NOT: The Jamesses.
Highest difficulty last: surnames ending in double-S, such as Moss. This is the same as surnames ending in S, but the doubleness of the S throws people off: it's "The Mosses," just exactly as with dress/dresses and kiss/kisses.
- NOT: The Moss', which makes no sense.
- NOT: The Mosses'; see The Sampsons', above.
If you are feeling confused, you can take comfort in the fact that you are obviously in the majority. If you want it boiled down to something simpler, remember this one thing: NO APOSTROPHES. Got it? NO APOSTROPHES. Not in your own name, either: sign it "With warm holiday wishes from the Jameses," not "the James's" or "the James' " or "the Jameses'," or, heaven help us, "The Jame's." Why? Because NO APOSTROPHES, that's why. We are only making things PLURAL (for more than one person in the household), NOT contracting words or discussing who owns what.
But again, my choice is addressing it to "The James family" and signing it "The Thistle family." Then it's no apostrophes AND no plurals. This also helped me with a former acquaintance whose family's surname was Spear, and who got very pissy each year when cards arrived addressed to "The Spears" (which is CORRECT) and she would say, "It's SPEAR, it's SPEAR, it's not like Britney!!" So I addressed my card to "The Spear family" and therefore did not get rebuked for being RIGHT.