First, you'll want to open your project. You'll land on the Project's Page & Survey tab:

In the Project Questions and Dynamic Content section, click on the black Add Content button. (If you're adding content to a topic, it will be in the same location, but under Edit this topic page.)

Click within the content box, and the content editor will appear:

Next, click the "image" icon in the editor:
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This will bring up the Media Library:

You can select an existing image, or upload your own. You'll also have the option to resize your image by right clicking the image and selecting a pixel value:
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Note: When resizing an image in PublicInput, be sure to click the "lock" icon to lock the image ratio and avoid image compression (a.k.a. the "smooshed" appearance.)

You also have the option to click the "Link" tab and add a hyperlink from the same Image Properties window:

Alternatively, if you don't have any image re-sizing to do, you can highlight the image in the content box and click the "chainlink" icon.

You'll then see the Link pop-up window asking you to paste in the URL:

Once you've added your link, click "OK."

Lastly, you'll need to click Save Changes in the content box:

You can preview how your link will display by clicking the View Live Site button at the top of the Project
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Related articles:

How to add content to a project

Adding custom embeds and code to your project page

How to create a link to a .pdf file within your project