Measuring is very easy really. If you can count you can measure. Here are some simple terms

dash – 1/32 oz
teaspoon – 1/8 oz
tablespoon – 3/8 oz
pony – 1 oz
jigger – 1 1/2 oz
wine glass – 4 oz
split – 6 oz
cup 8 oz

there are 3 common ways of measuring.

With A Jigger.

Jiggers are usually 2 sided with one side being larger in size than the other. They come in various sizes. Typically they are 1 and a half oz in size.

With 2 Fingers

There is nothing wrong with using a jigger and recommended at first, however over time you will get the hang of pouring and be able to use other methods.
The 2 finger method only requires you wrap your hand with 2 fingers at the bottom of the glass and pour til the top of your fingers. If your fingers are slim, leave a little air in between and if they are thicker, stop the pour just below the 2 fingers. The 2 finger method is fast and inconspicuous.

With a 3 count

Specifically a 3 count will also give you about 1 1/2 oz of liquor. This is only when you have speed pourers on the top of the bottle, just grab the bottle and turn upside pouring into the glass and count to 3. Using one thousand one, one thousand two, one thousand three so that you get 1.5 oz. Practice with water until you get the timing down and 1.5 oz.