Oh, you'll know when you find a Magic Plant. There's a noticeable sound and a popup window informing you that you've discovered one!

The message will look something like this:
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You have discovered the <name of Magic Plant>!

<Description of the plant's benefits>.

This effect is automatic and permanent.

The plant has been repotted in a golden pot and moved to your nursery.
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Once you close the window, you can go to your nursery (the selling area) and see the plant in the center where the fountain is.

The key to breeding the Magic Plants is to find a systematic way to cross-pollinate. Although you can find them "accidentally" by just breeding willy-nilly (I did that the first time, but it took 3 weeks of playing almost non-stop), you'll have more success if you approach your breeding in an orderly fashion. Many people have created spreadsheets, but you can take a simpler approach. For example, once you have upgraded your soil to support the rarest plants, try breeding one particular plant with each of the others that you've discovered. Then do the same thing with the resulting plants. Before long, you'll be seeing plants you've never seen before.