Eventing is a LOT of fun!! To get started I would find an eventing coach in your area, I googled "eventing virginia" and a ton of links came up, so that's a place for you to start. I would also ask around, talk to other horse people in the area (even if they're not eventers), inquire at tack and feed stores as well.
As far as getting started, step one would be finding a trainer in your area. I would also look on facebook for any local eventing groups and join them, get in there and start talking to people. I know there is a lot of eventing trainers in VA, right off you probably don't need to go with someone big name, I would look for someone who has a reputation of getting riders solildly started at the lower levels. If they have a customer base that is consistently doing well at the lower levels, even better!
You might be able to find someone in your area willing to trailer you to lessons and clinics and things, lots of people have an extra spot in their trailer, and if you offer to split costs and have a well mannered horse, a lot of people wouldn't mind filling it! Eventers in general are friendly and willing to lend a hand wherever needed! Renting a truck and trailer may be an option for you, as well as hiring a friend or someone at your barn who has a truck and trailer to transport your horse. I've been eventing since 2005 and still don't own a trailer, now we do have a truck though so we either rent or borrow a trailer, but before that I was just bumming rides with others from my barn or other eventers, or hiring someone to haul, I found placing a classified ad on websites and local eventing boards worked well too. It was a bit more work for sure, but it worked out really well! So it can be done, for sure!
Your trainer will get you started with the basics and the things you need to know for eventing. Getting out for some cross country schooling and a few clinics is a great way to get out and about and learn more about the sport. Eventers are big on clinics, there's no better way to get out and about to practice your skills in different places!
Your trainer will also let you know what "extra" things you'll need for eventing (medical armband, vest, watch, pinny, a good pair of cross country boots, etc) and what to expect at events. And when you go out to your first event, you WILL need that trainer to help you along and show you the ropes, let you know how things are going to work and help organize you. Many eventers choose to just get coaching at events, and some feel confident enough to go without later on, but for starting out that person who's been there, done that, will be SO helpful!!
There are lots of excellent websites and articles that have lots of great information on getting started in eventing, if you have time I definitely recommend googling around and doing some reading.
Hopefully that helps you out some:)