I've always found the photo capabilities of motorcycle forums to be limited. I prefer to use a proper photo sharing site and then just use links in the forums. That way if I get a new bike and move to a new forum I don't have to upload all the photos again.
I'm using SmugMug and I'm very happy with the service.
To answer your question, you type your message in the message window as normal. If you scroll down a ways you will see a red button that reads MANAGE ATTACHMENTS. Click that and a small window will open. You will have to stretch it a little to see some CHOOSE FILE buttons. Click on the first one, navigate to your pic and then click UPLOAD. After you have finished uploading the photos you want to post, click CLOSE THIS WINDOW button at the bottom. You will find some more text in your Message window. You can hit the PREVIEW POST button at the bottom to see how things will look. If you like it, just hit the SUBMIT REPLY button.
After all of that, I just noticed there is a feature below the Message Window that says DRAG FILES HERE TO ATTACH! Did you try that?
I know about the storage problem, but I just wanted to answer his question. I agree that an off-site photo sharing site is a better solution, but sometimes that isn't as easy to some people as it sounds either.