One aspect of comprehension is the knowledge that your students glean from what they are reading. While you don't want your students merely to do rote memorization of the material, at the same time, it is important for them to get the gist of the main facts and hold onto them. You should have this as a goal and occasionally have tests and quizzes to confirm whether students are absorbing the information. Depending on the students' age, these tests could be matching or multiple choice.
Understanding the meaning of a book, story or article is a central feature of reading comprehension and one every teacher should stress. This takes students beyond just information and requires them to really "get" the intention of the author. There are several ways you can address this with your students. You can have in-class discussions of the readings, which should quickly reveal how well they understand the material. Another approach is to have students write a synopsis of what they have read. If they can express the thought in a different way, this will demonstrate understanding.
Another useful way to see if your students are comprehending the material they are reading is to have them apply it in some way. With a work of fiction, one way to do this is to have them compare and contrast it with a similar work by another author or by the same author. With nonfiction, you might ask them to apply the ideas in an article to another similar situation or topic to see if the concepts the author present apply to it as well.
A final aspect of comprehension is the ability to criticize what you have read. Have your students write in-class essays in which they examine a work and give their opinions about it. For fiction, they could say how effective they think they author was in creating characters, plot or atmosphere. For nonfiction, such as an article, they could examine the arguments and opinions and present counter-arguments if they disagree.