Make sure you know what program the teacher is using at school so you can reinforce its methods. Otherwise, your child may get confused. Most teachers would appreciate sharing any information and resources with you. Also, check out websites from the program's publisher. They will provide additional help. Finally, get to know the reading comprehension terminology. Find out from the teacher some specific skills that need reinforcing, like context clues, inference or making predictions, among others.
Use a variety of texts. Don't be limited to just the textbook that is used in the classroom. Comprehension practices can be used with any book. Choose one that interests your child, like a comic book, or a non-fiction book about a hobby or game they are currently playing.
Set aside a specific block of time to help your child relative to their academic need. If they just need a little additional practice reading, then both of you can have a time of SSR (sustained silent reading). This need not be long; 15 to 45 minutes is sufficient. If your child needs help on a specific skill, like inferring or context clues, then work on that skill for approximately 15 to 20 minutes, then read together. Quality, not quantity, is what makes the difference.
Get others in the family involved. If there are older siblings who are willing, get them to help reinforce skills, even if they just read aloud to the targeted child. Hearing texts that are read in a fluent voice with good expression will help their own reading ability as well as augment comprehension. If there are only younger siblings, then have the child you are helping read out loud to them. This will give them great oral reading practice without the stress of being in front of peers as they would be in school.
Don't let an indirect teachable moment escape without utilizing it. For example, have your child read billboards while you are driving on the freeway. Have them identify words on signs that are unfamiliar to them, and have them make a prediction about what they mean. After they see a movie, have them summarize it for you, both orally and written. These are only a few suggestions of how you can use real life experiences to increase comprehension.