You have to apply via lottery in March. Only 300 permits are issued a day. We up our chances by every person in our party (6) apply for the dates we want. Sometimes we luck out and get multiple permits so we invite more people. Other times we strike out entirely.
Tons of people flake or something comes up so there is forfeited permits up for grabs via application also.
Then there is luck and a good attitude. Rangers hang out at the base of the subdome to verify permits. You can hang around there or just prior and ask groups that go by if they have any open slots in their party and ask if you can hop in with them.
It’s a fun one that I look forward to doing again.