You basically have two options - you can buy them, or grow them. If you buy them, be sure to seek out organically grown flowers free of any spray or pesticides. If you grown them yourself, keep in mind you'll eventually be consuming them, so treat them accordingly.
hibiscus, rose, rose geranium, violet, calendula, chive, basil, thyme, cherry blossom, zucchini blossom, and nasturtium. Keep in mind, not all flowers are edible, some are poisonous, and proper identification is essential. Again, not all parts of the flower are edible, and some varietals should be avoided if you are pregnant or nursing, so please read up with some of the references I link to up above. On the rose front, heirloom varietals are broadly thought to have better flavor and fragrance, with newer roses often bred for appearance rather than flavor (fragrance).
Once cut, I tend to keep flowers in clean water until I'm ready to use them. They typically last this way from 1-5 days, with regular refreshing of the water. I'll typically trim or pluck petals from the vase as I need them. If I get the sense I might not use them entirely while fresh, I make the move to dry them before they go bad. (instructions below)
This requires patience and a bit of space. I'll start by saying I haven't had luck drying flowers in a low-heat oven. The petals quickly lose color and vibrancy. Instead, I arrange them in a single layer on a parchment-lined baking sheet. Leave them for about a week, using your fingertips to toss them every day or so, or until dry and crisp. I usually wait until they seem completely dry, and then give them another couple of days to rid themselves of any residual moisture I might not be able to sense. At this point transfer to a tight jar or container.
Please let me know if you have other favorite edible flower ideas, uses, or references. I saw a rose petal paste the other day that looked incredible, and I'm always looking for other ideas, techniques to explore. On the list to try: Lilac Honey (thx Shari!) & Lilac Sugar, & chive blossom vinegar xo -h