One good tip I was given was to bullet point work experience. This makes it look neat, concise, cuts out all the unnecessary connecting words and stops you saying more than you need to. I just wrote "2 weeks at such and such a place" and then the dates. Try and make youself look into everything - research, small animals, large animals, exotics ect: Focus on veterinary things and then put in one paragraph about other activites to make you look well-rounded. Also, if you say you do or have done something, back it up by saying how it would make you a good vet and which skills it helped you develope. But make sure you don't repeat the same skills!
Don't worry about it being long at this stage - your finished piece will be completely different. I did like a million drafts! Oh, and try to have a good opening sentence, not just the old "I would like to be a vet because...."