“How soon would you be available?”
You're interviewing a candidate for a job. You think you might want to hire him, so you need to know when he can start working.
How soon would you be available?
You can politely ask someone when they can do something with the phrase "How soon would you be ___?" For example, ask a plumber to come to your house to fix a problem:
How soon would you be able to come out?
Or ask a coworker to send you a report:
How soon would you be able to send it to me?
Asking this way makes it clear that you want the action to happen soon.
You can say that someone "is available" if they don't have any other appointments or commitments at a certain time. Use this phrase to talk about people's schedules:
I'm available on Wednesday after 3:00, or any time on Friday.
When will you be available?
When someone is applying for a job, the date that they are "available" is the date when they no longer have to go to their previous job:
I'm available immediately.
I'm available starting next Monday.