How do I learn spelling?

English wasn't my first language but it's my better one. I didn't learn spelling since the language I went to school in has everything spelt how it sounds. I can read perfectly but no matter what I do my spelling is ATROCIOUS. I lose around 15-20% on my English tests on spelling but I just can't tell when a word doesn't look right. I also can't spell out loud and get the letters confused on longer words. For example I was asked to spell a word once in French and around the third letter I couldn't do any more of it. My reading is very clear and actually faster than most people, I just can't spell for the life of me. I have an important English test coming up so I'd like to get a good result. My teacher tells me to read over my work more and stop making careless mistakes, but it all looks right to me when I read it.