A Croquet picnic combines the idea of a pleasant picnic in a local park with a game of croquet to occupy the players between mouthfuls of cheese and sips of wine.
The basic idea of Croquet is to hit your ball through a series of hoops while helping out your team-mates and hindering your opponents. It's quite like a game of large scale snooker on grass.
There are four main types of croquet, Association (English), Golf, American, and Backyard. For beginners I would recommend the Backyard version as the easiest to learn and the most fun to play straight away. A good guide to the rules for Backyard Croquet can be found here.
If you are interested in the history of the game and a general guide to the different types and variants you can't go past the Wikipedia Croquet page.
Croquet can be played on just about any flat patch of grass which makes it ideal for your local park. Playing in a park also means that you can take along a picnic and a few bottles of white and make a day of it.
However you will need to buy, borrow, or steal a set of clubs and balls. Any decent sized sporting shop should sell croquet sets. Buy a good quality set if you can, as it will add greatly to your enjoyment of the game.
The other option is to hire the grounds at an established Croquet club. Many clubs, such as Elwood allow you to hire their lawns and provide equipment hire and sometimes instruction as well.