Head to Google Docs, open your document, and select the paragraph by dragging your cursor through the text. This highlights it in blue.

• Go to Format in the menu, move your cursor to Paragraph Styles, and pick Borders and Shading in the pop-out menu.
  
  When the Borders and Shading window appears, you can make your selections. To add a border, start by choosing the Border Width. You’ll then see the line locations highlighted at the top. Click to select or deselect the border Positions you want to use.
  

You can then use the drop-down boxes for Border Dash to pick a line style and Border Color to choose an option from the color palette. To apply shading to the paragraph, use the Background Color drop-down box. You can use shading with or without a border.

One more option is the Paragraph Padding at the bottom of the window. This lets you add more or less space between the text and the border or for the background color. When you finish setting up the border or shading, click Apply.
If you decide to remove a border or color you add to your paragraph, you can easily reset the changes you make. Select the paragraph and return to Format > Paragraph Styles > Borders and Shading. Click “Reset” in the pop-up window.