An experienced professional will chip or sandblast out the old plaster to leave the original concrete shell. A bond coat is applied and then topped off with one to two coats (or more) of new plaster tinted according to your preference.
It's not all sunshine and drink-sipping out there. You must also address the fact that pool's underwater surfaces can deteriorate over time.
Painting pools can get dusty, and they don't always bond to the plaster. You could also paint your pool if it is already painted. If the pool's surface is made of old plaster, I recommend hiring a professional to re-plaster it. Painting your pool plaster will not make you happy for long term.
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