The staff is read left to right: one note to the right of another means that it is to be played later. The vertical position of the notehead on the staff indicates which note is to be played: notes that are higher in pitch are marked higher up on the staff. The notehead can be placed in the gap between two lines, or centred vertically on a line. Each rise to the next position, be it line or space, represents a rise of one step in the diatonic scale. Notes which fall outside the range of the staff are placed on or between leger lines, lines the width of the note they need to hold, added above or below the staff.
The staff alone does not represent any specific notes without a clef, although a clefless staff may be used to represent a set of percussion sounds. The clef fixes one particular position as being a specific note, for example the treble clef puts the G above middle C on the first line up from the bottom.
Once fixed by a clef, the notes represented by the positions on the staff can be modified by the key signature, or by accidentals on individual notes. Unmodified, the positions on the staff give the scale of C major.
The application of a time signature groups notes on the staff into measures.
The musical staff can be thought of as a graph of pitch with respect to time; pitches are roughly given by their vertical position on the staff, and notes on the left are played before notes to their right.
Here is an example image with some typical music notation