I am on H-1B - what is the process to switch to student status?

Change of status to F-1: get admitted (about 2 weeks after a complete application), receive the I-20 (about 1 week), then file with USCIS. Regular processing runs around 3 months; premium is usually decided within a month for roughly $1,900 extra to USCIS. You keep your current status while it's pending. Nobody can promise the outcome - what we control is a clean, strong file.