I am a native English speaker- and sometime we also struggle to learn to spell. When I was in primary school they would teach us little tricks to help us learn. These helped to remember the basic rules that Goatish was talking about. I found that these helped: - "i before e, except after c" - For deciding if a word should have a double consonant in the middle, we were told a story. eg little, kitten, bubble The vowel sound is trying to squeeze through a closed gate. If there is only one consonant eg. rule, stone, lame then the vowel can get under the gate- as it is squeezing through it will make the long vowel sound. If you place a second consonant there then the vowel is stuck on its side of the fence making its short vowel sound. - Principle vs principal Principal has pal at the end- if you behave then your principal will be your friend. ( principle is the rule) I also learned a lot of mnemonics. eg. Betty Eats Cakes and Uses Six Eggs = BECAUSE eg. Lucy Ate Uncle Gary's Hat = LAUGH I have a few more of these sort of things up my sleeve. At the end of the day - there is no substitute for practice.

You can listen to mp3's and videos that have transcripts with them. Write out what you hear, pausing the audio/video so that you can type in a manageable piece at a time. Then check your spelling against the transcripts. And don't forget to look at how much you already spell correctly! Memorize the really irregular words (though, tough, thought, taught, ought) and the homophones (sew, so). Learn basic rules: when to double final consonants, when to change y to i, etc. Learn the pronunciation of common word parts. -tion, -ity, pro-, etc. Have fun!

practice practice practice. You can even use software that has a live spell check feature like Microsoft Word or Openoffice to type out and see youor errors as you type. then right clicking will show you corrections. Maybe use it like a diary every day to improve!

Just to complement Goatish answer... I used to read books listening to the audio of the books. After I had read a chapter, I would leave the book aside and play the audio alone, and I would pause sentence by sentence and then compare what I had written against what was written in the book. If the spelling matched perfectly I would go on. If not, I repeated the exercise as many times as necessary until every single word was correct. Maybe you could try that. It is a slow exercise, but it helped me.

Try using word games http://www.dailywritingtips.com/word-games-to-improve-your-writing/