How soon would you be (able to do something)?

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.

(someone) is available (on a certain date / at a certain time)

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.