How do you set up an apple 7 watch with a stand alone #?

Other than possibly using Family setup, I don;'t believe there is any way.

Set up Apple Watch for a family member - Apple Support

Also, see the reply to:

Will my Apple Watch have a different phon… - Apple Community

A few posts above javaliga provided a link which explains how to set up an Apple Watch for a family member who doesn't have their own iPhone --> Set up Apple Watch for a family member - Apple Support

Do you mean, not tied to an iPhone? If you do, that's not possible as Apple Watch is not a standalone device and whether you pair it with your iPhone or use a family members iPhone to host your watch, an iPhone is an absolute requirement.

The new Apple 7 (if purchased with the cellular capability) should be able to not require a phone to be carried at all times. You are supposed to link it up to a family phone and go through the family share process but then should be able to function alone. I am getting stuck on the icloud agreement page so hence searching for an answer..

That's correct. A cellular Apple Watch 7 when set up with cellular service does not need to be near the connected iPhone in order to work. But it has to be set up with an iPhone directly in the set up. Is the iPhone you are trying to use with you? It has to be at least for the initial setup. In other words, you can't be Virginia and the phone want to be connected through in another state.

Ask others and I have stated, the paired iPhone (i.e., its "own") share a common telephone number UNLESS you use the Family setup procedure. And in that case, you need a plan with a phone network carrier.