There's a post on Major Nelson's blog that describes how Gold will work on the Xbox One. It's well worth a read, as there are some nice benefits, though it's not all sunshine and roses.
Some of it is not too surprising. If you buy a game on your home console, anyone can play that game on that console, regardless of whether or not you're signed in at the time, and regardless of that person's account status (Gold, Silver, local-only). Also, any game that you've purchased, you can go to any One console, download that game, and play it, and the full version will be available to you and anyone else on that console so long as you are signed in and connected to Live. This is exactly how things work on the 360 today.
What's new is, if you have Gold on your home console, all accounts on that console will have access to Gold features, a new feature they call "Home Gold". Also, if you sign in to Xbox Live on any One console with your Gold account, everyone on that console will have access to Gold features as well for as long as you are signed in. This is a nice new feature. Back when we had the 360 and I had the only Gold account, it meant features that are (inexplicably) locked to Gold members could only be accessed by me. My wife grew tired of having to sign in to my account just to use Netflix, and it was for that reason that we got a Netflix-capable Blu-ray player — she turns it on, presses the button for Netflix, and she's good to go, no ifs no buts no coconuts.
What's kind of disappointing is that the Gold Family plan is going away. That means I will not be able to pay a little extra and give three of my family members full access and privileges to Gold wherever they are.
For the One, this may not be that big of a deal in our house. We will only have a single One console in the house for a while, so everyone will have Gold access. However, if my son wanted to play at a friend's house who didn't have Gold, he would not be able to take his Gold privileges with him. Or, if we bought a second One for a playroom, he'd similarly be out of luck. (Major Nelson seemed to indicate on Reddit that the Home Gold feature would be available on all Ones in a house, but he quickly backtracked and said he would need to investigate to be sure.)
It is worth noting that my kids may not be all on the One right away. For one thing, $60 for a controller is a little tough to swallow. For another, we won't have a vast library of One games at launch, and there are still tons of games on the 360 that my kids love to play. (They even play original Xbox games still.) Since Home Gold is a feature exclusive to the Xbox One, Gold will not be available to my kids that will no longer have access to my Family plan. So for those who try to follow Mattrick's advice and stick to the 360, that's a feature that's going away.
I've seen comments further on this issue that I didn't even think of. Broken or separated families use the Gold Family plan to keep family members all on Gold when they are not in the same physical house and all on one console. There are other features that, as of yet, there has been no word on replacing — things like being able to transfer Points (soon to be real money) between accounts for content purchases, for example.
In any case, my kids are now being forced to decide whether they want to spend their own money to continue Gold for their own accounts on the 360, or to buy a controller for the One. Now, fortunately, they have some time to decide, as Microsoft just sent me an email saying when they convert everyone to individual accounts, everyone will have Gold until the original expiration of the Gold Family subscription, plus three months each. But still, it's sad to see them taking away features from the 360 in what seems like an effort to push people over to the One.