Newspapers can provide simple reading activities. While an entire article is beyond a child's comprehension, there are plenty of words in the paper that the child will understand. A child with a highlighter can go in search of words in an article. Start with basic words that are common: the, and, her, his or run. Select an article that is likely to contain the words that the child picks and let her highlight them. Having many different colored highlighters makes for an appealing final product.
Begin with an old book that can be marked up. Ask the child to circle each word in the story to help him understand that words are strings of letters and separated by a space. Point to the different words and let the child read them. For each word he can read, see if he can find where else it is written in the story.
Children are often with parents on shopping trips and they see the signs throughout the shopping plazas and malls. Let them start making word associations by giving them a "shopping list" that contains common words typically seen in stores. A five-word list is perfect. It can include words like: exit, entrance, store names, sale, push, pull and so forth. Read over the words with them so that they are not just searching out strings of letters. When they find words, let them read the word as they cross it off the list.
When reading with a child, a great concluding activity is to have them write a storyboard that details what happened in the story. As an example, allow children five pages or a piece of paper with five boxes and ask them to draw a picture to show the first big part of the story, the second big part and so on. Have them write the ideas or fill the ideas in for the child.