Pressing flowers doesn't provide as much instant gratification as some other activities, but you can enjoy it in multiple stages: first gathering and prepping the flowers, and later using the finished products to make other crafts.
Gather fresh flowers from your garden or the wild -- just not anyplace picking might be prohibited. There are lots of good candidates including (but not limited to) pansies, daisies, carnations, poppies, hydrangeas, delphiniums, marigolds, geraniums, tulips, violas, petunias, baby's breath, zinnias, miniature roses and forget-me-nots. You can even press ferns, leaves, grasses, herbs and stray petals.
To do the actual pressing, you can use a store-bought plant press or use materials from around your house to make your own. The simplest method is to take a phonebook, dictionary or other heavy book and place parchment, newspaper, tissue paper, coffee filters or other unglazed, absorbent paper between two pages. Put the flowers between multiple sheets of this interior paper and close it carefully. If you don't care much about preserving your book, you can even omit the extra paper and let its pages do the work. Place something heavy on top to weigh it all down and let it sit for days to weeks. You can also make presses out of layers of plywood or other sheet wood, cardboard and paper, with rubber bands, bungee cords or something else to hold it all together.
It's best to start with flowers that are collected during dry conditions, not after rain or dew. Cut off stems and leaves, unless you want to incorporate those into your crafts. Place your flowers in whatever positions you want. You can do multiple flowers at a time, but make sure they are relatively similar in size and aren't touching one another. If your flowers are too large, you can dissect them or remove parts to make them thinner. Leave the press (makeshift or otherwise) in a well-ventilated place. Check it periodically and carefully replace the surrounding paper if it is moist and the flowers aren't dry. After anywhere from a week to four weeks, your flowers should be nicely dried and ready to save or use. You might be able to speed up the process by heating flowers in a press made of cardboard and paper in the microwave.
The finished flowers can be used to decorate candles, soap, jewelry, eggs, cards, bookmarks, boxes, photo albums, scrapbooks, lampshades and a host of other things. Or you can glue them to paper and frame them as art pieces. The research into different types of flowers should prove educational, and you and the kids can have loads of fun creating floral art with real flowers.