The 3 reasons why students don't read in English
They are lazy:
It is certainly true that some students are lazy. They think just coming to class two times a week and doing the homework that we set them is enough (and some don't always even do that).
They are busy:
This is especially the case with kids around exam time and adults who have demanding jobs. Although some may use this as an excuse, for many of our students, it isn't.
They can't find appropriate or interesting material:
It is easy for us to tell them to just read something in English on the web or buy a novel, but it can be difficult for them to find something which is right for their level. The majority of articles that they will find on websites for native speakers will be too difficult and confusing for them (even for students who have an upper-intermediate level). In addition, it is also surprisingly difficult to easily find things to read in English that are interesting.
And like everything in life, if something is difficult, boring and takes a lot of time to do, you not are likely to want to continue doing it.
How to get your students to read
When you are thinking about ways of getting your students to read more in English outside of class, you need to take into consideration these three main reasons why students don't do it and try to overcome them.
And below I will suggest a method which I have found works really well with my students and what to do for getting the reading material you'll use with them.
Give them something to read as homework
Instead of telling them to find something to read in English, give them an article to read as homework once a week. It doesn't have to be a printed copy, you can just give them either a PDF file or the URL/web page address of an article you want them to read. Give this to them in addition to the normal homework you would normally do.
You'll find by doing this that many of your students will do it. But to make sure that the majority do, begin the following class you gave it to them by getting them to talk about what they read in pairs or small groups (it also helps their speaking too). Once they know they always have to do this, the majority of even the lazy or busy students will regularly read the article you give them.
Finding the material to give them
As I mentioned above, one of the main reasons students don't regularly read in English is that they can't find material which is right for their level or interesting. So, take responsibility for finding it for them.
Although there are some free reading resources on the web for English learners, unfortunately in my experience most of the material which they provide is far from ideal. Examples of two such websites which I have used in the past are Breaking New English and News in Levels. They are ok and the vocabulary is appropriate for people learning English. But in my opinion their articles are too short and they cover topics which are generally boring (that's what my students have told me).
I stopped using both with my students after a couple of months. I still recommend my students, especially intermediate and lower levels, to use the articles on these websites outside of class. Unfortunately, most of them seldom do.
There is one English learning website which does provides some longer articles, VOA (Voice of America). And although I still use some of the articles from it with my students, the majority of the articles they have aren't really that interesting (according to my students). So I wouldn't recommend that you only just give them articles from this website to read.
This creates a problem, you are not going to be able to find many good articles (and by good, I mean interesting) that have been specially written for English learners to use with your students.
Fortunately, there is a solution. But it requires you to do some work yourself.
Adapt articles yourself
I would recommend that you use articles which have been written for native speakers and adapt them yourself (changing the vocabulary and the length (around 800 words is perfect for students with a level which is intermediate or above)) for the level of the students you are going to be giving them to.
It does take time to both find articles and then adapt them for your students. But once you've got the material, you can use it for years in the future. So I think it is worth the effort.
To help you find articles to use with your students, have a look at the below websites (or sections of websites) which I frequently use to find the articles which I adapt and then give to my students:
In addition, you could search on Google/Bing for topics which you think your students would be interested in (e.g. will we live on Mars?, why do people have tattoos?) and you should be able to find some articles that way.
What topics to use
When choosing the topics of the articles you are going to give your students, you have to consider whether they'll find them interesting or not. Think about things which they'll have an opinion on (e.g. how to be happy, are selfies a good or bad?, is global warming happening? etc...). You may not get it always right at first, but you'll soon begin to find out what kinds of things your students will find interesting and which they won't.
In addition, I wouldn't recommend using news stories that much. Your aim is to create material which you can use with your students for years to come. So, for the majority of the articles you give to your students, choose ones which are 'evergreen' (which means that the topic of the article will be relevant and interesting for the students you will use it with in 5 or 10 years time).
Also, try to choose topics on diverse topics (giving them articles to read on the arts, science, sports, social issues etc...). By doing this you will broaden their range and knowledge of vocabulary, which is essential for them to improve their English.
There is one topic which I personally recommend that you don't give them any articles on, and that is religion. I unfortunately did once and it caused some problems for both me and damaged the relationship of some of my students in the class which I used it in. So, stay away from this topic.
An alternative to producing them yourself
The one downside is that it will take you quite a lot of time to do (to think of topics, find the articles and then adapt them). In my experience, it took me around two to three hours for each article I used on average.
So, if you're busy or prefer to spend your free time doing other things, I have a solution for you. I have produced two PDF eBooks with 50 long reading texts and vocabulary exercises (one eBook for intermediate/FCE level students and the other eBook for upper-intermediate/CAE level students) which you can use with your students to get them reading.
Giving my students articles to read at home (and subsequently talk about in class) has greatly helped them to improve their level of the language. And I strongly recommend you do the same yourself with yours.