How does a conventional rate-and-term refinance work?
A new conventional loan pays off your current mortgage at closing, and from that day forward you make payments on the new loan instead. The new loan can carry a different rate, a different term, or both, and that's the whole transaction: no cash comes out beyond paying off the old balance and the costs of the new loan, per the Fannie Mae / Freddie Mac Selling Guides.
One thing to know up front: there is no shortcut version. FHA has its Streamline and VA has the IRRRL, both of which skim the paperwork for borrowers already in those programs; conventional loans have no equivalent. A conventional refinance is a full application, underwritten like a purchase: credit, income, assets, and generally a new appraisal. That's not a flaw, it's just the process, and it means your approval and pricing get built from your file as it stands today, not as it stood when you bought the house. The trade runs both ways. If your credit or income has improved since you closed, full underwriting is where that improvement gets to count.