My DDs are almost 9 and newly 6. The info below applies to both of them. (DS, 3.5, is just now learning to read.)
I assign books (usually novels) for reading as a subject, done three days per week. Usually it's a chapter or two per assigned day - depends on how long and how dense the chapters are. Sometimes they really like the assigned book and will read more than that at a time or will ask if they can read extra at bedtime.
They read together from a science encyclopedia each week as an intro to that week's topic.
I try to have an outside reading for science, history, or both each week. These are generally not novels, but shorter books that they can read in one sitting, or else I direct them to choose a certain amount from the book to read.
I don't feel like I have to do any more than that, because beyond those things, they are reading PLENTY in their free time. I do the "reading as a subject" thing to make sure they are reading a wider variety than they might choose on their own; frequently, they'll choose to reread books they've read for school reading later on.