First of all, in Classical Music we have the following pitches that are equivalent to the white keys on a piano: A, B, C, D, E, F, and G. The black keys on the piano are A-sharp (or B-flat), C-sharp (or D-flat), D-sharp (or E-flat), F-sharp (or G-flat), and G-sharp (or A-flat). What are these sharps and flats? They are half-steps. The distance between A and B is a whole step, and there is a half step in the middle, called A-sharp or B-flat. Sharps are notated as # and flats are notated as b. Thus, A-sharp is A# and B-flat is Bb. Sharps indicate that the note should be raised one half step in pitch. Flats indicate that the note should be lowered one half step in pitch. If A=1 and B=2, then A-sharp=1+0.5 and B-flat=2-0.5, meaning A-sharp and B-flat are equal. There are two exceptions, however. The distance between B and C and the distance between E and F are already half steps. This means that B-sharp equals C (and C-flat equals B). Likewise, E-sharp equals F and F-flat equals E. Another thing is that after G-sharp, the cycle repeats and we return to A. This means that A-flat equals G-sharp. once we repeat to the next A, we will have completed one "octave." This may all be very confusing, but the following picture may help make it clear:

Now that we know about the staff, rhythms, rests, and the actual notes, let's see how these notes are written down:

As you can see, the staff has five lines, and a note is either on a line or on a space between two lines. When you see the treble clef at the beginning of the staff (the squiggly symbol before the 4/4), the note on the first line is an E. The note on the space above the first line is an F, and the note on the second line is a G. This is the basis of Classical Music notation, and is the standard that has been used for writing music for the past four-hundred years.
Here is how note with sharps and flats are written: