Sinks are held in two ways:
1) Clips under the sink hold it to countertop.
2) Adhesive caulk.
Consult installer who will know exactly what adhesive is correct for your top.
And what procedure will minimize clean-up and not damage top.
To do this yourself:
Take photos of everything before starting so you know how it goes back.
Dry off countertop and then let dry for couple hours, then outline location of sink with masking tape.
This will help you reinstall sink in exact location and minimize caulk clean-up after smoothing out caulk bead with wet finger when sink goes back in.
We use wet/damp sponge to help caulk >> here's how it works: Wet finger on sponge, smooth caulk short ways with finger, wipe excess on paper towel, wet finger again, repeat slowly around sink. Remove tape immediately after caulk is smoothed.
Disconnect tubular drains at P-trap.
Disconnect disposal from sink basket and lay down inside cabinet.
Or you can leave disposal connected to sink, if you're strong enough to lift sink and disposal together. In that case, disconnect electric wire and dishwasher tube.
Turn off water. Disconnect supply lines at shut off.
Lift out sink.
Use pry bar and pry against wood paint stick.
Use bottle jack or car jack from underneath, and go real slow.
Have cardboard boxes where you can set sink up off floor.
Setting sink up will let you work on heavy sink and won't scratch floor.
Remove old caulk with single-edge razor blade, or scraper. Go slow not to scratch anything.
Apply new, continuous bead of caulk and set sink in place.
Sink will have to be held tightly by someone while working underneath.
Attaching disposal to sink basket without moving sink will the challenge.
Attach water supply lines, turn on water and check there are no leaks.
Lift disposal into place and attach with ring... leave attachment ring bit loose until tubular p-trap is aligned.
Any tubular pipes that were moved must be taken apart, cleaned and reassembled.
Rubber washers are replaced with new ones.
Plastic washers are cleaned and re-used. Tapered end of plastic washer goes away from nut.
We use rectorseal on all tubular joints when re-assembling under-sink pipes.
Smear it all over each washer and p-trap joint before attaching nut.