What's the best way to extract broken glass from my sink?

First of all, very, very carefully. If you could get some leather gloves it would make the chore much easier and safer. As long as its thick leather you shouldnt has much trouble picking out small shards.

Pick up large pieces carefully. Then dampen some cotton and wipe gently on surface (so not to scratch porcelain. The small shards and specks of glass will adhere to cotton. Do several times. Examine sink then from all angles w. a flashlight to see whether there are any more glints. If you can wait until surfaces are dry, then vac. Or just keep sponging w. cotton until it comes up clean. Careful about splinters (maybe wear gloves.)

Yrs, Heloise

Don’t panic.
From years of bartending experience…
Get your worst rag. I mean the oldest and ugliest on you’ve got. With one end of the rag, gently wipe the glass pieces into one corner of the sink, then slowly up the side of the sink, and then wrap the tail end of the rag around to cover and throw the entire package away. Now, not only is your sink glass-free, but you’ve gotten rid of that nasty rag. What were you thinking keeping such an ugly rag around?

also, u might want to check the trap- under the sink. Put a small bucket under the drain, unscrew and clean out the trap now. You don’t want to run into glass when the time comes when someone loses a precious necklace down the sink.

Vacuum. I use mine for everything from bugs to glass!

When your done rinse the micro splenders down the drain.