To add to Strange's post...
I have worked for three trainers.
Two of them are big names in eventing. However, the first trainer I worked for was just local and didn't do the high levels. She taught me so much though! Honestly working from the ground up is the best thing to do.
Grooming for a trainer at shows will also give you a lot of amazing experience. I love it! Especially when the horse does well :)