Go through essays you've written; highlight words that you repeat/are really basic, and get out the thesaurus. (I just type in Google, 'define [the word]', and it lists synonyms which you can click on for definitions. Or the Microsoft Word thesaurus. Remember that synonyms rarely have exactly the same meaning... so check their definitions, and keep an eye out for seeing them elsewhere.) Make a word-bank with lists of similar words grouped together. Keep referring to this, especially after writing more essays - when editing, try substituting words from your word-bank just to get practise with them.
Reading more widely is of course/unfortunately the best way... but takes time. Especially read other people's essays, and highlight/steal any words or phrases you love!
Stick up words that you think you could use heaps on your bedroom wall. Dream about them.
