When you place a dot after a note in sheet music, you are adding on half the value of that note.
Example 1: There is a whole note worth 4 beats, it is then dotted so we add on half of 4 which is 2, so a dotted whole note is now worth 6 beats.
Example 2: There is a dotted half note. A half note is normally worth 2 beats, so when you place a dot after it you add on half the value of 2, which makes it 3 beats long.
Example 3: There is a dotted quarter note. A quarter note is worth 1 beat, when you place a dot after a quarter note you add on half the value. Half of 1 is half, so a dotted quarter note is worth 1 and a half beats.
A tie is shown by a curved line from one note to the next. When dotting notes you can only add on half the value of that note. Yet, when a note is tied to another you are adding on the value of the note it is tied to.
The first note is played and the second note is not sounded, but the value of that note is added on to the first.
Example 1: The first note is worth 1 beat (quarter note), the second note is also worth 1 beat. When tied the first note is now worth 2 beats.
Example 2: The first note (which is placed on the third beat of the bar), is worth 2 beats (half note) the second note it is tied to is also worth 2 beats, and the third note tied is worth 1/2 a beat. Since all three notes are tied, the first note is now worth 4 & 1/2 beats. In this example you can also see how to make a note last for a certain length of time over a number of bars.