OPT expires on 1st June.Extension and H1 Visa application

I am on OPT of 12 months and applied for H1 Visa from 1st April 2013 .My OPT expires in 1st June. Can I stay on in USA till my H1 is processed.How do I apply for cap-gap.

You will automatically become eligible for cap-gap when your H-1 gets filed w/ COS in April. Once you get the receipt, you can let your school advisor know about it and they will update the SEVIS record.

Note that if H-1 gets denied, or you do not make through the cap, then you will not recive cap-gap and will have to rely on OPT extension (if eligible).