The main thing. dorfmouse, is to stay relaxed. If this feels natural to you, you could introduce your first piece only and stand to receive your applause; then announce your second piece before re-seating yourself at the piano.
I went to a school recital recently, and a pianist played three pieces. She announced the first before sitting at the piano, then took applause still seated and announced her second and third pieces from the piano stool.
Basically, it doesn't matter too much what you do, as long as you feel happy with it. The audience will be happy whatever you do, provided you don't seem awkward or nervous. The secret of performance is putting your audience at their ease so that they are receptive to the music, so relax and enjoy it!