Start with small amounts of text at an easy level and then increase the length and difficulty of the texts you read.
Tiny Texts is a great little blog that lets you listen and learn English in little bits at a time.
Breaking News English provides short texts and podcasts on current news stories organised in 7 levels (similar to our 7 levels of General English).
News in Levels and Read it English each begin with a test of your English level and then shows you articles to suit your level. At News in levels you can also listen to the news and follow up by finding a speaking partner in the Skype or chat section. Read it English offers interesting articles beyond regular news and you can provide feedback at anytime to get more difficult articles as you progress.
Teacher's tip: the more you read, the better you get so read for fun. To stay motivated, look for texts about things you enjoy and read widely. If you prefer reading from a book, visit the Learning Centre.