Plecostrum, I usually use whatever I have around to make my pickling brine. I use about 1/2 cup (of 5% acidity) vinegar per pint, a clove of garlic, some dillweed or seed, and that's all you really need. You can add peppercorns, bay leaves, mustard seeds, beets (for color), onion, or anything else you have around. Fill your jar with the seasonings, eggs, and vinegar, top it off with hot water, tighten the lid, and let them marinate for at least a week in the fridge.
Also, when I'm feeling lazy, I just throw some boiled quail eggs in a jar of leftover commercial pickle juice - Delicious!
-Zay