Learning the notes on the piano.
There are any number of 'games' one can play to learn and then test for knowing where the keys are and finding them quickly. Spelling words, hopping up all the, for instance, 'Fs', finding notes with eyes shut, running to the other end of the room and back straight to a named key.
Notes on the stave/sightreading.
I would like to say here that I don't especially like (and don't use myself) the mnemonics (Every Good Boy Deserves Fruit...etc) as by the time you have remembered which sentence goes with which stave and whether it applies to the lines or spaces, you may as well just learn the note! It seems more to learn rather than less. I teach one note at a time, and when there is a lapse I prefer the idea of landmark notes from which others can be worked out, or directional observation of how the notes are moving on the stave.
Useful tools and games for reinforcing the position of notes on the stave are flash cards; writing own compositions (4 bars or so) each time a note is learnt, using the notes thus learned so far (if written in a book this could be a wonderful diary of progress and creativity); sight-reading; writing a story around words that we can find on the piano and writing these words on manuscript paper.
Sightreading and note reading should be an ongoing and important part of daily piano playing, and recognising the feel and sound of rhythm and note patterns on the music is a vital part of this. Games that include naming notes, naming and finding notes, sightreading short pieces, finding the skips and steps/broken chord patterns/scale patterns in the music, clapping rhythms, writing rhythms that you clap (one bar in length) and clapping short rhythm patterns, singing notes in step and skip and scale and chord patterns and then guessing which you are playing, will all help with internalising what they see so that they can translate it from the written page to the piano.