Availability is a loaded word, at least in business terms. It means so much more than just being there; any decent worker can should be there for their employers, subordinates, and co-workers when they're needed. SuperCompetent people need to be keenly aware of time management and being there too much. After all, we each have a limited amount of time, and we're not going to get any more.
Saying yes to everything will leave you so overburdened that you won't be available when people really do need you—except on those rare occasions when you manage to clear a task off your schedule. You require some flexibility, which means you not only have to learn how to say no to some requests (or creatively negotiate them somewhat), but you also need to learn how to deal with the distractions and diversions commanding all your time.
You don't have to do everything, by any means; the idea is to be SuperCompetent, not SuperHuman. Superman is a fantasy, and even if he wasn't, you have to remember he's supposed to be an alien from another planet, not a human being. Knowing how to delegate and/or outsource tasks whenever you can—and having the wisdom to do so—is a must.
You'll also need to learn effective scheduling techniques to make life easier for you and everyone else, and hone them to maximum effectiveness, so things don't get out of hand. The same is true when it comes to meetings. Meetings are a prime example of the tendency for tasks to expand to fill the amount of time ...