First, make sure the Google Docs ruler is visible.
Click "View" and make sure "Show Ruler" is checked. If it isn't, click on it, and the ruler will appear beneath the menu bar.
On the ruler, at the left margin, there is a light blue rectangle atop a triangle:
The light blue rectangle (▃) represents the location of the First Line Indent.
The light blue triangle (▼) represents the location of the Left Indent.
On the ruler, hover the cursor over each shape, and its function will be displayed.
First: Select the text you want indented. You can select a single paragraph or multiple paragraphs at a time.
Next: On the ruler, drag the ▼Left Indent (light blue inverted triangle ▼) to the right as far as you want the text to be indented. As you will notice, the ▃ First Line Indent marker (light blue rectangle ▃) will come along for the ride, and all your selected text will move to the right.
Finally: Drag the ▃ First Line Indent marker (light blue rectangle ▃) back to the left margin. It will move independently, and your hanging indent will be created.
When the cursor is within the indented area, the indent icons will now look something like this: