Kids,even toddlers, are instinctively doing the scientific method. Think back to your first science class, the scientific method is laid out as observe, question, hypothesize, predict, test, conclude. How many times have you seen a toddler walking around asking Why? Why? Why? about everything they encounter? I know I lived through it for years, and still get the why question from King Boo. Boom! Scientific method :) Kids are awesome at it, they are constantly observing the world, always asking questions, and often, they are experimenting to see what will happen. They will do the same thing over and over again to see if the same results occur each and every time. Innate scientists! So how can you encourage this behavior in a safe, fun way? These are the techniques I have used to keep King Boo interested in science.
Ask questions! They do not have to be answerable or even incredibly deep. Something such as "Why do you think X is happening?" can be a great science conversation starter. Or when your little one comes and asks you WHY?, turn it around and go I don't know.. what do you think? :) You might be surprised by their answers, and even if it is completely wrong and totally insane be sure to tell them that's a great idea/hypothesis! For older kids try pointing them to a place where you can look up the answer together.
Compare and contrast! It's a common practice in biology, such as compare and contrast animal cells vs. bacterial cells or plants vs. animals, etc. Pick two things or group of things to examine what is the same and what is different. It can be anything, from cat vs. dog, Lego vs. Lincoln Logs, Action figures vs. Barbie, orchid vs. sunflower, etc.
Make science special! I bought him the Learning Resources Primary Science lab because it comes with test tubes, beaker and Erlenmeyer flask that are good for little kids hands.This way when we are mixing red baking soda water with yellow vinegar into an orange volcano it can spew out of a Erlenmeyer flask. It just "looks" more science-y ;) Now you do not need to have special equipment, just make a big deal about let's do SCIENCE! Set up a special spot and do a simple experiment.
When you do any experiment, I highly encourage you to use the following format. With younger kids just talk about it, with older kids have them write it! There is a great quote from Mythbusters "The difference between screwing around and science, is writing it down." So first no matter what you are doing have him/her write/answer these statements before/during/after the experiments:
The observation/question/point is _________.
My hypothesis/guess/prediction) is __________________. (before)
At first _______________ happened. In the middle _____________ happened. At the end ________. (during/after)
I conclude _______________. (after)
After you get comfortable with an experiment you can try changing things to see if they can figure out what is the critical step that makes the experiment work. A fun one to try is Mentos in Coke, spoiler, it EXPLODES everywhere so do it outside!! You can investigate different properties with different solutions, so try it with Coke (original experiment), Sprite (is it the color?), flat Coke (open it the night before, is it the bubbles?), water (is it the sugar?) that makes the explosive reaction occur.
Where can you do this? EVERYWHERE! Go on a nature walk and compare grass with a bush, look for bugs, look around an ask questions, count the number of animals you see, make an identification key for different trees what makes each distinct so you can identify them again next time, etc. At the grocery store compare nutritional information or fruits/veggies. At home, baking soda volcanoes + color mixing, track the weather for a week and make a chart, extract strawberry DNA, investigate what materials will make static electricity (rub a balloon vs aluminum foil on their hair, what sticks?), etc.
Some good general supplies:
Optional but a lot of fun for little kids: Learning Resources Primary Science Lab but you can use glasses/measuring cups for the same things
Books that I like:
175 Science Experiments to Amuse and Amaze Your Friends by Brenda Walpole is my favorite, it's out of print, but our library has it so I would encourage you to check your library.
101 Science Experiments by Neil Ardley looks like it has fun things in it as well though we have not used this book.
The Animal Book by DK Publishing is full of beautiful pictures and great information on all sorts of animals!
If there is a specific topic you are wanting to explore check the best science resources list from the National Science Teacher's Association and Children's Book Council, each book is fantastic: http://www.nsta.org/publications/ostb/ostb2014.aspx
There are lots of good kits out there as well that include the random/crazy chemicals that are harder to acquire. I have been really happy with the Magic School bus and Scientific Explorer (Poof-Slinky) brands. Do not just limit yourself to the kit either, try changing variables and see what happens to your results.
No matter what you use, be sure to have fun!