If you look carefully enough at printed music, you will often see dots all over the place. While those dots do look random, they are most certainly not. Every dot on every piece of music has meaning. The dots that are situated near a note can be confusing to some learning to read music.
If a note has a dot with a semicircle situated directly above the note, like this:
This means that you pause on the note or notes that is directly underneath. What happens when you pause on a note or notes, you are actually interfering with the regular beat or pulse of the piece of music. The best and probably most famous example is in the Happy Birthday Song. When you get to the part where you sing the birthday person’s name, the music sort of grinds to a halt before recommencing singing (and recommencing the beat), with the last line of ‘Happy birthday to you.’
Sometimes there will be a dot directly above the head of the note (when the stem of the note goes down) or directly below the note head (when the stem of the note goes up). It looks like this:
These dots indicate the notes are to be played staccato, which means they are short and detached. In terms of achieving staccato notes on the piano, it requires the player to gently bounce their finger off the note or notes.
If you see a note or notes with a dot and then a line immediately below the dot (or above the dot, when the dot is above the note), then that indicates the notes are to be played mezzo staccato, which means moderately short and detached. I tend to think of mezzo staccato as a half-hearted effort to play staccato – it is not really smoothly blended into the surrounding notes but it’s also not really crisp and short sounding. It is somewhere in the middle. Also, if you see a phrase mark (see here http://pianoforretirees.com/what-is-the-difference-between-a-tie-a-slur-and-a-phrase/) above notes with dots directly above or below the note head, then this also means that these notes are to be played mezzo staccato.
Notes can also have dots that are situated on the right hand side of the note head are called dotted notes. What these dots do is affect the length of the note. The dot on the side means that the note is now 50% longer, so a dotted crochet (quarter note) is now worth one and a half beats and a dotted minim (half note) is worth three beats. Theoretically, any note can be a dotted note, but most of them are dotted crochets (dotted quarter notes) and dotted minims (dotted half notes). A dotted crochet looks like this:
Even though it is not that common, there is such a thing called double dotted notes, which is indicated by two dotes very close to the right of the note head. The first dot extends the note by 50% of the original note value and the second dot adds a further 25% of the original note value to the length of the note. For example, a crochet (quarter note) is worth 1 beat, a dotted crochet (dotted quarter note) is worth one and a half beats and a double dotted crochet (double dotted quarter note) is worth one and three quarter beats.