Finger crochet can be a fun activity for kids, being quick to learn and very easy to do. (Technically it's more finger knitting than finger crochet, but the name has stuck! ) Any yarn will do, but for learning you'll want something cheap and easy to grab, like a mid-weight knitting acrylic. In the US, Red Heart makes perfect stuff.
To start finger crochet, wrap the end of the yarn around the thumb of your off hand (for most people that's the left; lefties should use the right instead). All the thumb has to do is hold the end for the first few rows of work, so the yarn doesn't have to be tight or even knotted. Now, with your palm facing you, weave the yarn through your fingers as follows: behind the index, in front of the middle, behind the ring, around the pinkie, in front of the ring, behind the middle, in front of the index. You should end up with a row of loops around your fingers. Repeat the weaving sequence again, so that you have two loops on each finger.
On your index finger, take the bottom loop (the one closer to your palm) and lift it up over the top loop and over the top of the finger, leaving it on the back of the hand. Repeat for the other three fingers. That's the first row of work. From here, it's a simple matter of repeating the weaving sequence and lifting loops. You'll only have to weave once for each row after the first, because there will always be one loop left from the last row. When your chain of stitches is as long as you need it to be, cut the yarn and pass the end through the last four loops to finish it off. The chain will look bunched up and cramped until you pull it out straight, so don't be put off by the messy-looking mass of yarn that will develop on the back of your hand for the first few rows.
Now that you've produced yards of the stuff, what should you do with it? For one, it's handy for tying things: leashes for pets, curtain tiebacks, hanging wreaths or other decorations on the door, that sort of thing. If your chain is dense enough, you can also coil it and sew it to itself to produce rugs, placemats, trivets, potholders, and so forth-produce a denser chain by using thicker yarn and/or pulling the loops tighter around your fingers. You could use a chain in a festive yarn in place of ribbon on a gift, or press short pieces into service as headbands or hair ties. In a fine yarn, you could even use it as shoelaces! The possibilities are nearly endless.