They would announce it. The existing shareholders would be contacted and offered (usually) a slight premium over the market share price. You are not required to accept the offer.
It is possible for them to do the buyback as market buy orders through their transfer agent, but they would be foolish to do that IMO, as it would just cause the market price to shoot up, and the company would end up spending way more money for the same number of shares. And, of course, if the share price shot up like that, everybody and their brother would place a market sell order as soon as the momentum stops and the price started to roll over, which would crash the price back down.
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