Some of the forums will allow you to directly upload images; most will not. There's a weird workaround if you want to avoid 3rd party sites. (I feel like I'm writing a clickbait article )

1. Open a draft post in one of the forums that does allow you to directly upload images.
2. Upload your image. This will generate an image url for that picture on this website.
3. Copy that image URL and BBCode. The post itself can stay in your drafts. (You might be able to delete it, but I haven't tried.)
4. Open a new post in the forum you want to write your actual post.
5. Paste the Image URL+BBCode into that post.
6. Write your post and publish it with the picture.

That's how I got the picture uploaded for Murkmire Forum Bingo here: https://forums.elderscrollsonline.com/en/discussion/441706/murkmire-forum-bingo