Let's assume your child has found a genre or author of books that they find exciting and engaging, what next? Well, it sounds obvious but let your child read! If they really love the book they might want to find a quiet spot and get stuck in. Even if it's an old favourite, children love the story and don't mind too much that they know the ending.
Reading in itself will help with comprehension because children will usually learn to fill in the blanks and work out the meaning of difficult words but encourage them to talk to you and ask questions if they need a little help.
Some people like a quiet space to read, while others can read anywhere and ignore what's going on around them. Bedtime is often a favoured time to read for adults and children alike, as a way to relax and unwind from the stresses of the day, so having a bookshelf loaded with good books in your child's bedroom is a great idea.
Bedtime is also an opportunity to spend some time reading together with your child. We're often told to help comprehension by asking our child questions as they read, but try to do this with some empathy as we don't want it to turn into a question and answer session or a school lesson. By all means discuss what a difficult word might mean and consider people's feelings as you read as typical comprehension questions will ask about word meanings and emotions.
An overall understanding of what you are reading is also important. In comprehension tasks there is often a relatively small passage taken from a larger piece of work, such as a book. Whilst it's not expected to know anything else about the passage than what's presented, it's good to try and think about the meaning of the passage rather than just focussing on one sentence at a time. Some questions may need you to think about the story itself and perhaps ask what might have happened before or after the text provided.
Remember, reading should be fun! Try to get your child to look forward to your reading times together rather than them thinking it's going to be another interrogation session. You'll find your own comprehension skills improve and you might be surprised how much you learn!