Everyone has really wonderful ideas, but I thought I'd throw out what we do if it might be helpful. My boys have very short attention spans, which can be helpful, actually, but my oldest does ask an awful lot of questions.
We go for walks in the woods and practice observing a lot. We dig under rocks and in creeks and in mud and look at bugs and we do a LOT of googling. I also get lots and lots of children's nonfiction books out of the library about anything and everything: experiments, color, light, dinosaurs, evolution, spiders, animal encyclopedias, early history, etc. They seem to be mostly Usborne, Scholastic and Dorling Kindersley books, but they have those on every subject imaginable. That way we just have stuff on hand to discover and browse at our leisure. As homeschoolers, we get books for 6 weeks, which means I can get several bags full and they can peruse casually and reject things they don't care about (fyi - my boys are not reading, but they look at the pictures and pick out "stories" including nonfiction at bedtime).
We have a membership that gets us into the science center, the natural history museum, the botanical gardens, and the zoo and we go to lots of nature centers in our metro parks regularly. I end up reading a lot of the plaques that describe things out loud and we play with the experiments and things. When out of town, we visit children's and science museums. We volunteer in our local foods movement for the food co-op and a community supported agriculture group, which gives an even more direct meaning to our lives. We also have chickens and bees at their grandparents' house and we grow things ourselves.
We're very casual about it all, but we do spend time looking things up when need be, watching videos on YouTube and reading books, as well as doing lots and lots of "sciencey" things that satisfy a natural curiosity. I'd like to get a microscope next so we can take a closer look at lots of the things we discover. One other resource we've discovered is that we carry a camera with us most of the time so when we're in the woods and we see a bug, we'll take a photo of it, then post it on BugGuide dot net
to get an identification if we can't find it on our own.
We've also done experiments like growing borax crystals and playing with corn starch goop and growing our own butterflies.
When I write it all out like that, we sound very sciencey. I always thought we were far more art-focused. Hmm. I guess it all kind of blends together.