Grapes, unlike many other fruits, will not ripen any further once you pick them from the vine. This means you must ripen the grapes fully before you pick them. Otherwise, you will be stuck with sour, hard grapes that will not please your palate. You cannot control the speed at which grapes ripen, but you can do a few things to help speed the process along and know when the appropriate harvest time approaches.
Locate any overhanging bushes and trees that block sunlight from the grapevines. The fruit does not require sunlight to ripen, but the leaves do require sunshine. Overhanging foliage blocks necessary light and will slow down the ripening process.
Prune all light-blocking foliage with pruning scissors or a pruning saw. Be careful not to damage any other fruit-bearing trees or bushes if you want to produce fruit from multiple sources.
Collect samples of the grapes on a weekly basis during the growing season. Avoid grapes from the ends of the plant or from odd vines that do not resemble the majority of the other vines. Grapes start green with a high acid content and low sugar content. If you prefer purple or sweet grapes, wait until the grapes turn purple to start testing. There is no universal determination of ripeness -- it is personal taste. The longer the grape remains purple, the higher the sugar content becomes.
Harvest your grapes when your samples conform to your desired taste.