My almost three-year-old daughter is reading through some second grade readers, and I just ask her a few simple questions at the end of each day's lesson, like: "What happened to Ruth's and Naomi's husbands?" or "Where did Naomi and Ruth go?" Sometimes she answers correctly and sometimes she doesn't. If she doesn't, sometimes I have her go back and read the sentence that tells the answer, but really I don't try to press it too hard. I found the less I interfere (both while she's reading and after), the more she engages with the text.
Really I think the trick is just letting them read read read. The more they do it, the more they will comprehend. DD and I have our daily 10-20 minutes of reading in a reader, and beyond that I put books in her hands whenever I can and just let her discover them for herself. For a long time she would just look through the pictures or even just goof off pretending her books were plates of food or something else. Eventually she started looking at the words and enjoying them by herself. I really noticed her beginning to improve when I'd occasionally throw in a second reading time with mommy--like if she woke up early from her nap--but instead of reading the reader, we'd pick one of the children's books from her shelf that had been read to her before. Some of these books she knows very well, and I was surprised at how much work it took her to read them herself. BUT I found them highly motivating for her. Something seemed to click like she started to understand what reading by herself could really do for her. We don't do this every day, but I wanted to mention it, because I noticed she began to really take ownership of reading when we started doing it.