Dawn,
Yes, an acceleration provision typically means that the stock options will fully vest in the event of a takeover (most commonly, because employees are concerned that the new firm may fire the old staff and thus cause the option value to be lost). Of course, whether the options actually have value or not (i.e., whether the stock price is high enough for them to be worth something) is another matter!

As for what typically happens to the value of a company's stock after it is bought it, the answer is that it really depends on the deal and the situation. In some cases, the company is bought for cash - which means all of the stock is sold at the agreed-upon price, and after that it's up to you to reinvest your proceeds! In other cases, the shareholders in the original firm may receive stock in the new firm - which means you're subject to the vicissitudes of the new company's stock (in the same way you were with the old company's stock), and it's really a matter of the financial outlook for the new company.

I hope that helps a little!