To help you get started, here are 5 tips you'll find quite useful.
Read (读) the headlines. Just read the headings and the titles of the articles. Practice reading. Since there's no pinyin or zhuyin to help you, practice reading the bigger font first. This will help you from getting discouraged. Don't force yourself to read the whole article the first try.
Choose (选择) your favorite section. Whether it's the section on travel, sports, culture, lifestyle or world news, you'll find reading the papers more enjoyable when you're reading something that interests you. Once you build up that habit then, broaden your scope and try branching out to other sections.
Go for words first instead of sentences. I use to count how many words I can recognize in a paragraph. It really encourages me to learn faster and read longer paragraphs. When youfirat start reading, read the words first. It doesn't always have to make sense. Just practice reading them and understand how they are used. Then, slowly look up the other words or go over them while looking for context clues.
Check the English translations. Check their website. Most of the Chinese papers have English translations readily available in their website. You can use it to check if you understood the articles perfectly. But remember, don't compare it word per word. It doesn't mean that the second sentence in the Chinese article corresponds to the second sentence in the English article. It doesn't work that way.
Take it slow. Start reading one article at a time. It's not something that you can learn overnight. It takes time for you to be familiarized with it. Don't worry when you can't understand the article the first try. Start reading the words first then, the whole sentence. Before you know it, you can fully understand a whole paragraph or even the whole article.