CPT: how long does it take if I get hired in April

I applied for a nurse externship for this summer. Interview in March and hosp lets me know in April if I got a position, start externship in May. Question is, if they hire me in April, is that enough time to apply and get an CPT to start work in May?

Is there a form the hosp has to sign for the CPT?
What are the steps and how do I state I am an F1 student and need CPT?
Also, what do I have to get from the hosp and college for the CPT?

Tks