How do you control the portion of text, or excerpt, under links in search engine results?

So if someone 'Googles' a keyword and Google finds a web page ranked high for that keyword, Google will try to find that keyword and its surrounding text, on that web page, to use for the excerpt.
The excerpt of a web page search result changes based on the keyword searched for and it's surounding text. If the search engine can't find the keyword on the web page, the web page description meta tag content will be used.
If there's no keyword on the web page and no description meta tag, then the first few lines of text output by the web page will be displayed as the excerpt.

My recommendation is to make sure your website has a 'description meta tag' using the keywords you've optimized your website for.

If you have a WordPress website and the custom theme doesn't have options to edit the description meta tag you can alter it manually by following these instructions.

Edit the description meta tag of your WordPress website

1. Log into your WordPress website admin.
2. Click the 'Editor' link under 'Appearance' on the left of the page.
3. Click the 'Header' link on the right of the page.
4. Enter in a description meta tag or edit the one present
   Example: 
   

   <meta name="description" content="WordPress Tutorials">

5. then click the 'Update File' button.