Octopus is an eight legged mollusk popular in Mediterranean and Asian cuisines. It can be tough if over cooked and there are a lot of methods for tenderizing, which include pounding and boiling with wine corks, which contain an enzyme that helps break down the meat. While those methods work, the most important element of cooking octopus is to simmer it for just the right amount of time, too little and it will be tough, too much it will shrivel, dry out and get tough again.
That said, there are no exact rules for timing. A good starting pace is octopus should cook about 15 minutes per pounds, but often the timing will be longer longer the larger the octopus. After simmering for the appropriate time, check the meat with the sharp point of a thin-bladed knife; when it cuts easily, the octopus is done. Remove from boiling water and either cut and use immediately in whatever dish you have planned, or plunge in ice water to stop cooking, then refrigerate for use later.
Octopus is commonly sold cooked and refrigerated, so you may want to choose buying it in this form to save time and effort with largely the same outcome.