I searched I swear! How do I add a photo to a thread?

When you start a post/thread, or reply to a post, then at the bottom of your post is the option to check "Attach a file after posting".  However, there may be a file size limit of what can be uploaded.

Additionally, you can sometimes copy/paste into the post of some simple stuff, for example I have copy/pasted some of the information below your avatar from my Windows 7 environment using Mozilla Firefox 25.0.1 using my mouse, to the following, below:
Champion
10163

Dallas, TX

Bronze member

Lastly, there is a menu bar and icon bar above the post (using Windows and Firefox and hovering the mouse over the icons you can find "Insert/Edit Image", which is between the little "chainlink" icon and the "text color" icon).  You can add an Internet image or BT photo by providing that photo's/image's URL, for example:
1). Click on the "Insert/Edit Image" button.
2). In the "Source" field, type in copy the URL, for example "http://thepetcollective.tv/wp-content/uploads/2013/08/hump-day.jpg"
3). Click OK.
4). Depending on the size of the image, or if the image is publicly-accessible/not blocked, then the image will display in the post, as noted, below:
 

I hope this helps.

In that case, you need to change your settings, 

1. Click on your name in the upper right ("Hello, KSH!")
2. Choose Settings
3. Click on Forum Settings
4. General
5. The second option is "Use rich text editor for blog and forum posts?" - Select Yes.

I believe that is how you get the formatting options, including the button to insert an image.  This only works if the image lives elsewhere on the web (say, in your BT album), because really you're just putting in the link location.  If you have the actual image file, then the "Attach File after posting" option is your best bet.