Learn how to add a hyperlink to an image or text in email templates

To hyperlink an image in an email template 
 

In Salesforce Classic

1. On the page where you add the content or the body of the HTML Email Template, add the link you want into the HTML text. For example: www.salesforce.com.
2. Highlight the text, then click the link icon on the Formatting Control and then retype the link address in the 'destination path' field on the pop-up window. Then click OK or click Save.
3. Highlight the working link in your HTML email.
4. Click the image icon and select your image.

In Lightning Experience

1. Click on the App Launcher.
2. Enter Email Templates on the 'Search apps or items' box.
3. Click on Email Templates.
4. Click on All Email Templates and select an email template from the list.
5. Open the template then click on Edit.
6. Click on the Source button to view the HTML code that makes up the template, then include the following code in the location desired:

<a href="Link URL">
<img src="Image Address" />
</a>

Or, simply click the image icon within the template to add the image with the upload option. 
 

7. Adjust the size if necessary and select Save.

To hyperlink a text in an email template
 

In Salesforce Classic

1. On the page where you add the content or the body of the HTML Email Template, highlight a text.
2. Click the link icon on the Formatting Controls ribbon and enter the URL on the pop-up dialog box.
3. Click OK to save the link.
4. Click Save to save the template.

In Lightning Experience

1. Click on the App Launcher.
2. Enter Email Templates on the 'Search apps or items' box.
3. Click on Email Templates.
4. Click on All Email Templates and select an email template from the list.
5. Open the template then select Edit.
6. Click on the Source button to view the HTML code of the email template.  The below code will insert a clickable link to a website location for the text you have entered. 
7. Click Save.

<a href="Link URL">link text</a>

See HTML Links on Hyperlinks on the w3schools site for more examples and further information.