Selected examples from the video:

Although font sizes can be changed in any cell, for the purposes of this "How to" only Text style cells are used.

Create a new Text cell by selecting Text from the Format ▶ Style menu, or use the keyboard shortcut indicated in the menu:

Type in some text:

To change the size of all fonts in a cell, first select the cell by clicking its bracket to the right:

Select a new font size from the Format ▶ Size menu:

The text is now in 18 point font:

You can change the size of subsets of characters in a similar way. Simply select the characters and change their size in the Format ▶ Size menu.

Here, part of the text was selected and then changed from 18 point font to 14 point font:

You can also use the keyboard shortcuts listed next to Larger and Smaller in the Format ▶ Size menu to change the font size.

In some instances, you might wish to see larger font sizes when working in a notebook, but not when printing. In such cases, use the Window ▶ Magnification menu:

Magnification can also be controlled with the drop-down menu in the lower-right corner of your notebook:

If you have a number of instances in your notebook where you have to change the font size manually, you can consider the option of creating a stylesheet that defines the font size. Stylesheets in the Wolfram System offer very precise control over various aspects of text formatting.