Not sure how many people care about this, but I'm gonna share it anyway, just in case some folks may need it:
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the 60-day grace period is automatic, you don't need to apply for it or anything.
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the grace period starts the day after termination of employment, instead of the date when employer withdraws your H1B
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during the grace period if you can find another employer, it will be a simple transfer process, once the transfer petition is filed, you can start working for the other employer.
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after the grace period, either you leave the country, or change status (consult visa attorney to make sure you know the potential consequences of this action). With the new status, you can still look for jobs, but won't be able to start working until a new H1B petition is approved.
That's about it.
Best wishes to those who are impacted.