Hi Ryan - welcome to Arbtalk!
I would suggest looking up a few local companies in your area and asking if you could go in and do a few days work experience with them to get a flavour of what it's all about. If you like it, then it would be best to get some training to pass the necessary NPTC tickets for chainsaw use and tree climbing. Once you have them you shouldn't find it too hard to get some work. For a while you will probably be dragging branches and feeding a chipper but that's how we all start.
Alternatively you can go to college and do something like the National Certificate in Arboriculture which would give you some good background knowledge as well.
If you go to www.trees.org.uk
there is a page on careers there that shows some of the different routes you could pursue.
Hope this helps? Post away any more questions - we are all here to help.