How do you get someones social security number to collect a judgment?

Get a lawyer, it's a ton of paperwork and the details of what is required to file claims like this vary from county to county let alone state to state.

If you already have the judgment, then you can get a court order demanding the information required to collect it. Once you have a court order, the debtor has to turn over all the information you need or be in violation of the order. This can result in additional sanctions against the debtor, including fines and/or jail time.

Without the judgment and court order, you have no legal right to this kind of information.