Here you will find online resources to improve your spelling:
The Survey of English Usage, based in the Department of English Language and Literature at UCL, has developed a free app to improve English spelling and punctuation:

english spelling and punctuation

Find more details on their website:

Find here some suggestions made by the University of Toronto to improve the spelling of university students:

Other resources:

If you want to know more about the complex history of English spelling, have a look at these books:
spell it out
David Crystal’s Spell It Out
Simon Horobin’s Does spelling matter?