If you want to show a screenie, just upload it to any half-decent free image host; I personally prefer Photobucket. If you haven't already, you'll need to start an account, of course.
Once uploaded, your pictures (on just about all the services I'm aware of) will have a way, either under the pic itself or by clicking a button, to display the various ways you can link to that image; you want the one in IMG tags. For example, the following pic:
is displayed using the tags:
[URL=http://s196.photobucket.com/user/Bozobub/media/errorerror.jpg.html][IMG]http://i196.photobucket.com/albums/aa38/Bozobub/errorerror.jpg[/IMG][/URL]
The URL tags on the outside make the entire picture "clickable", so users can jump directly to the original pic's source by doing so. If you want to disable that behavior, simply delete everything
outside the IMG tags, like so:
This is displayed using the tags:
[IMG]http://i196.photobucket.com/albums/aa38/Bozobub/errorerror.jpg[/IMG]
Sorry, dunno why the code tag is italicizing that o.O' , but notice how no direct link shows now when you mouse over/click the image?
If you go back and look at the tags in a post's preview, btw, you'll notice that this forum adds image height/width info:
[URL=http://s196.photobucket.com/user/Bozobub/media/errorerror.jpg.html][img width=206 height=124]http://i196.photobucket.com/albums/aa38/Bozobub/errorerror.jpg[/img][/URL]
This is NOT something you have to do yourself; it's automatic. You can safely ignore it.
If you don't want the image to display until someone WANTS to see it (as I did above), btw, which is polite and saves everyone load time and bandwidth, simply put everything in spoiler tags:
[SPOILER]Everything you want to hide, including any tags.[/SPOILER]
Note: Tags don't have to be capitalized, I just did so here for clarity.
Hope that helps. Now you can show screenies (and any other image) w/o using attachments. This also works on most forums that use phpBB (as opposed to HTML) formatting commands, assuming IMG tags are enabled.