Field Day is an emergency preparedness exercise/ contest that is held the last full weekend of June each year in the United States and Canada. It is sponsored and maintained by ARRL. Points are awarded in a variety of ways, but the general idea is that the station should be set up in short order, operate only on emergency power, and a number of other activities related to emergency preparedness. You could operate on VHF only, but most of the action will be on HF.
There are a number of ways to participate. Some people participate as individuals, but most people participate in clubs. I strongly suggest you find a local club that is participating, and go join them. You shouldn't need any equipment, although there usually is a talk in frequency available if that helps, so a mobile rig can be useful, along with an HT. You've already found the list of clubs participating, feel free to join one of them. Or if you have a club you've participated with in the past, then find their field day site. If you are a new operator, there is a station that most clubs will have called a GOTA station, where there will be someone who will help you to get on the air. There might also be sign ups to operate one of the main stations. You can also sit as a secondary operator, helping to log the contacts and otherwise helping out. You might want to contact the club, or look at their website for more information ahead of time.
For reference, here's my club, if you're in the area, feel free to stop by and say hi! Most of the club listings will look pretty similar to this one.
Loudoun Amateur Radio Group
38668 Sierra Lane
Contact: Norm Styer