Improving your English spelling
Misspelled Words
You could start here and look over a list of the 250 most misspelled words.Of course, there may be different spellings (e.g. American versus British). At this site there is a list of over 450 of such words.
Not all words carry the same 'weight'. A mistake in a common or 'easy' word (when words are grouped into levels, it is not according to how simple they are, but rather how often they normally occur) makes a worse impression than getting a word like monosaccharide incorrect.
It therefore pays to make sure that you are familiar with the 1000 most commonly used words, (this site is also a good place to work through these lists) - then the second thousand, then the third. Another good group of words to work on next would be the academic word list, especially if you are doing tertiary study.
Lots of useful spelling rules and tips
Certain spelling rules may make it easier for you to remember how to write a word. The 'I before E' rule is probably the best known (if not the best applied!). The '-ible and -able' question is largely one of memory, but it can be tackled by using a rule about word roots. One issue that is partly a spelling issue and partly grammar is the formation of plurals. There are rules about when to use capitals, when a letter is doubled, adding -ing, -ed, and -ly, and about which letters to use for which sounds. It is probably best not to go overboard with these.