Can someone with experience help me understand what happens when...

Can someone with experience help me understand what happens when a takeover offer has been agreed?

For example. I hold 'X' amount of shares. The share price should go up once the offer has been signed for example to $1. Do I then sell my 'X' amount of shares at $1 or do I hold them until the code '4DS' is taken off the ASX and it becomes some other code on the American exchange?

I only ask because I once held an ASX listed company that transferred or was bought out by one in America and it was a total pain in my rear end to sell my shares on the american exchange. A lot of people sold out on the ASX before it transferred over but unfortunately I didn't because I didn't know what I was doing.

Thanks.