This sentence has actually used a structure 一...就..., which means "as soon as". "一" means "一旦(once)". The whole sentence can be divided like this: 她/一旦/有时间，就/看/英文书. Once she has time, she reads English books. or She will read English books as soon as she has time.

"有"means "擁有" to have. She reads English book once she has time.

Well it means'as soon as I have time' or 'as soon as I'm free/available '. Eg:I will drop by you as soon as I have time'我一有时间就来看你。Do you understand now?Ask me again if you still have some problems;)