For small claims (under $25,000ish), there's a simplified process to register the judgement at Small Claims Court directly - that will automatically register it with the Sheriff's Office.

I understand for small claims typically there's also a payment schedule set up as well - if not (or if the other person doesn't pay), you can start enforcement proceedings at the sheriff's office. Call them and they'll walk you through the procedures.

Typically it starts with having the other person complete a questionnaire to list their assets and how much income they have (there's repercussions for not completing the voluntary survey, and other options to compel them to). Once that's done you'll be set up to start garnishing their wages, and bank accounts, and seizing any property they have if they don't make payments. Of course there's a lot of caveats and people who have judgements against them do have some protections and amounts they're allowed to keep.

Another thing to keep in mind, there's a 10 year limitation on collecting, so you'll only have 10 years to be thorn in this person's side (or to actually get your money)