Did you know that extra virgin olive oil is a fresh fruit juice? Yep! And, like any juice, you don't want to save it for a rainy day; you want to savor it before it goes bad!
The first and most important way to ensure your olive oil is fresh, is to buy extra virgin produced during the most recent harvest season. So if you're purchasing an oil produced in the northern hemisphere (the US, Europe, etc), the most recent fall (typically November) would be the date you want to see. Conversely, if the oil is coming from South America or Australia, the recent harvest would be summer. Note that there can be a lag time between when the oil is harvested and when it hits the market (for example, in December and January, you likely won't come across any of the new season's oil just yet).
Buyer beware: many bottles won't include a harvest date, and will instead print a "best by" date or perhaps a date for bottling. These aren't the dates you are looking for! If all you can find on a bottle are these aforementioned dates, then your best bet is to look for another EVOO, as, in general, a high-quality extra virgin will always make mention of the harvest date.