Essentially you can use quail eggs just like you would chicken eggs. That means you can fry them, boil them, pickle them or scramble them, depending on your preferences. Some people love making miniature deviled eggs with them. Kids also love them because of their tiny size. Seeing a few miniature fried eggs on a plate can be pretty funny for a child.
They are slightly more flavorful than chicken eggs, and also have a greater yolk-to-white ratio, meaning that there is more yolk than white in the egg. Nutritionally, they are also higher in nutrients than chicken eggs, having more protein and a higher level of B-vitamins per gram. 
You can usually find them at Asian grocery stores. Some larger grocery stores in urban areas also carry them. They're really quite pretty to look at with their speckled shells.
In terms of recipes that you can make with them, here are several that you may want to try:
This potato salad recipe from Yotam Ottolenghi calls for 15 quail eggs, which seems like a lot, but really isn't that many when you consider how small they are. It also includes potatoes, fresh basil and parsley, parmesan cheese, pine nuts, garlic, olive oil and other seasonings. It sounds absolutely delicious, and might be a fun alternative to traditional potato salad if you are looking for something a bit more sophisticated:
Herb-Rolled Quail Eggs
These herb-rolled quail eggs are boiled, peeled and then rubbed with olive oil and rolled in za'atar seasoning, a Middle Eastern spice blend made up of sumac, thyme, roasted sesame seeds, marjoram, oregano and salt. Here's a link to the recipe for the seasoning:
And here's a link with instructions on how to apply the seasoning to quail eggs:
Hopefully that gives you some fun ideas to try!