This is a great question. There are many things that you can do to help students to construct meaning through reading and writing. Let me suggest a few ways.
First, you can ask students to try to find the main point of a passage or text. This is probably the easiest thing to do. Have them also give you a few reasons why they they this is the main point of the reading. They can even write a short essay on this.
Second, you can ask students to trace themes or motifs. This is a little more sophisticated. Ask them to explain how these motifs are used and developed.
Third, you can ask them to think about symbolism. Are there any symbols and if so, how do they work in the text?
Fourth, when the students are really good, then you can ask them to read some literary theory and have them apply this literary theory to texts.
Fifth, another fun exercise is to do comparisions and contrasts. Have them write an essay on how two peices of literature intersect. Or have them look at a theme in two different stories.
As you can see, the list is really limitless.
Depending on the age of the students, also consider Kagan (look up online if unfamiliar) activities. If students are at the beginning of learning how to construct meaning through reading and writing, have them read a short answer question, put them in groups of four, give them time with each contributing thoughts to their group using pens of different colors on their own paper, and then constructing a group answer together. That is the answer presented to the group where you can let the groups give constructive criticism about the answers and you can show them how changing just a small part would make the answer better. From this small beginning, you can stretch to a short reading piece from which they must find the main idea or proof of a question you give them from the piece, all the way to the Socratic Circle. To me, everything depends on the abilities of the students you are teaching and the age and readiness for the kinds of activities you want them to try. Success is the goal.
Another activity you could use is something called a Socratic Circle. This takes a lot of preparation time on the front end to set it up. You could google it or if you would like more information about it, I'd be happy to share it with you.