While I'm not an expert in coding myself, I have found a simple way for you to insert an image into your notification templates, by using this code here:
You'll want to replace the imageurl section of that snippet, with the URL of your image. The easiest way to get a URL for your image that you wish to use, is to go into Settings > Files in your Shopify Admin, and hit Upload Files. Upload your image in this section, and you will see that it gives you a URL. Simply copy and paste that in place of the imageurl of that link.
Alternatively, if you don't find this to work, there are a few apps from our Apps Store that can help you customize your notification templates, without the need of editing HTML. A few I've found that seem to be quite popular, are:
Hope this helps!