Water pumps have been made, in one form or another, for centuries. Hand-held models are easy to make, and are a fun craft and educational project for you and your kids, teaching both problem solving and some of the principles of hydraulics.
Cut a piece of 2 1/2-inch-thick PVC pipe to about 12 inches long. Cut a small circle about the width of the PVC opening out of a flat, flexible piece of rubber. This will serve as a flapper, just like the one at the bottom of a toilet tank. Leave a slight tab about 1/2 inch long on the edge of the rubber.
Use a waterproof marine glue to glue the tab of the circular piece of rubber to the inside edge of the PVC pipe, just near the end. Score the point where the tab connects to the rest of the flapper.
Remove the cap from the top of an empty plastic 2-liter soda bottle. Now cut the top off the bottle. Use the marine glue to glue the bottle top to the outside edge of the PVC at the same end the flapper is attached to.
Attach caps to the ends of another piece of PVC pipe that will just barely fit inside the first PVC tube. Now glue a series of felt strips near the bottom, in layers one atop the other, until you have something that just barely fits inside the first PVC tube, thus forming a seal. Then grease them up with vaseline. Glue a plastic strap to the cap at the other end to serve as a pump handle.
Cut a length of garden hose to 20 inches. Use a drill to cut a hole smaller than the diameter of the garden hose in the bottom of the outer PVC pipe. Glue the hose to the pipe over the hole you just cut.
Cut another flapper out of rubber, but this time make it slightly larger than the end of the garden hose. Glue the tab to the outside edge of the hose. When it dries, flex the flapper until it rests near the end of the hose. Place the end of the water pump in water, and pull up on the handle. When you do, the suction will open the large flapper pulling in water, while closing the smaller flapper. Then when you push down, pressure will close the bottom flapper, while opening the one at the end of the hose, and the water will come out of the hose.