It is not always easy to split all the skills into separate entities and practise them individually but you can build up a catalogue of tools and apps that you regularly turn to for specific tools. In my recent blog post I summed up a few useful tools for listening and I would also turn to these for reading practice.
Now, with a more direct focus on the skill of reading and comprehension here's a summary of some of the tools and apps that I might turn to. Quizlet would be my first port of call if I want to start building up a foundation of vocabulary knowledge. Quizlet is available as a web-based tool and as an app and can be embedded into a VLE such as Wikispaces. The flexibility of this site is such that you can include pictures, use lists created by others or create your own lists. For instance, it is quite easy to find long lists of examination vocabulary at every level and every exam board and these can be accessed by anyone (try this link for I/GCSE vocabulary) Obviously this is excellent for revision purposes or preparation for a particular practice paper. This tool is not restricted only to vocabulary for reading comprehension; it works as well for listening comprehension too. As mentioned all levels can make use of this excellent tool and it would be possible for students to input their own vocabulary as well which would provide a further challenge for some.
Duolingo available on the web and as an app is very versatile offering translation exercises and transliteration of spoken text to written text which requires a grammatical understanding and it provides excellent online reading practice. There are a vast array of texts in many languages that can simply be read or translated. An added benefit of this site is the ability to upload your own text from the internet and discuss any issues concerning the text or language with other interested parties and translators.
My final suggestion is Metro News. Many of us have seen these newspapers clogging up the gutters outside stations at the end of a busy day. However, the papers are available online (and as apps) around the world in a variety of languages (the main page has link to all the other portals) and the language is accessible to students in years 12 & 13. As a newspaper, of course, there are not any specific exercises, these are for us to create but we can then tailor them directly to suit the needs of our students. Each country has a regional version of the paper and within these articles can be found on the usual topic areas (headline news, economy, sport, health and so on).
These are just some of what is available - there are plenty more. What's your favourite?