These two words are pronounced the same way, but they have very different meanings:
Stationary = not moving
Stationery is a general term used to describe writing paper, pens, pencils, envelopes, etc.
We think the best way to remember this is: "Stop writing!" which is what you hear at the end of exams.
Alphabetically, stationary comes before stationery. Stop also comes before writing... So when you stop, you're stationary. When you're writing... you use stationery!