Beginning students
I use Faber Piano Adventures All-in-One Adult method books--Levels 1 and 2--with beginning students. These books, in addition to Faber Adult Classics Levels 1 and 2 and Faber Adult Popular Levels 1 and 2, provide the beginning student with a solid foundation in note reading, time signatures (3/4, 4/4, and 6/8), accidentals, basic rhythm and note values, and an introduction to the foundations of good piano technique.
The beginning student will be introduced to one octave major scales. A scale book is essential. I recommend Faber Piano Adventures Scale and Chord Book 2 for beginners. However, any basic scale book is sufficient for most students.
Intermediate students
When students complete Faber Piano Adventures Levels 1 and 2, they are considered early intermediate. At this level, lessons focus primarily on repertoire. While I mainly recommend and assign classical pieces, students are welcome to pursue working on pieces outside of the classical repertoire. All intermediate students will be working in a leveled repertoire book series--either Succeeding with the Masters Festival Collection or Keith Snell Essential Piano Repertoire. These books introduce the intermediate student to classical pieces from four periods: Baroque, Classical, Romantic, and Contemporary.
Intermediate students will continue to work on scales--both major and minor (natural minor and harmonic minor)--with a goal toward playing all scales in four octaves.
Music Theory
I believe that a basic understanding of music theory is essential to the developing pianist. Knowledge of scales, chords, and functional harmony is important in order to better decode, understand, and express the music you are playing. Some resources I use and recommend:
Fundamentals of Piano Theory by Keith Snell and Martha Ashleigh (A series of workbooks, leveled Preparatory to 10)
Elementary Rudiments of Music by Barbara Wharram (workbook)
musictheory.net is a good free resource for basic music theory concepts.