The Time
Music sounds - as they heard in compositions - are organized in tempos and rhythmic structures and we call: Time.
The time signature - on the first staff to the left, shows us how the time is organized - within one measure - into meter unites, and their qualities.
For example: If the Time signature shows 4/4; the upper 4, means that you will have four unite-meters in one measure, while the lower 4, means that each one will last a quarter.  Or if you have 3/4, the upper 3 means you will have three unites-meter in a measure, the lower 4 means that each one will last one quarter, etc.

The Beat
Without knowing or understanding too much about times and time signatures... we can always feel the music's beats. The feeling of the beats is our immediate self-reaction and it change accordingly to the music changes and its styles.
We can easily follow it as our leg as it moves up and down as we listen to the music. That is why I strongly recommend adopting the BEAT as the principal measurable time meter. It is easier to do it that way and you can be your own teacher just by moving your leg up and down (...in fact we shall say: down and up because we will always start from up-leg to down).
Please, look at the animation below: we are getting a "V" as we move our leg up and down.

Notes and rests duration
See how we can measure the notes' duration just by using the "V"
as it shaped by our leg's movement.

Click each of the note's heads below to hear theirs duration... When you hear the sound, try to fit in the "V" leg's movements accordingly to the beat numbers.

DOTTED NOTES 
A dot, next to the note head, at the right - refer to the note's duration! The dot means that you will have to add duration to that note. The edition will be half of the note's normal duration:

More... for practice...