There are two basic approaches: inserting a URL that points to an image that's already out there on the internet, or uploading a photo of your own (or possibly one that you found online, but saved to your own computer).
I assume you're asking for the first case.
First thing you want to do is find the picture in question. Let's say I want to link to a picture of an apple pie (mmmm). So I go to Google and find a website with a picture I like. How about the photo from
this page?
So I visit the page, right-click on the picture, and click Copy Location (I believe.. sorry, not using Safari at the moment). In Internet Explorer, you right-click, hit "Properties", and it'll show you the image URL, which you can copy/paste.
The image URL for the photo I found is this:
http://kitchenparade.com/uploaded_images/Kitchen-Parade-2007-American-Apple-Pie-400-735267.JPG
Now, armed with that information, you can click on whatever "insert image" button your blog or forum interface provides. For example, here on MacRumors, there's a little button labeled "Insert Image". The icon looks like a yellow postcard with a mountain on it. When I click the icon and paste the URL, it inserts the image:
<img snip>
The general idea is the same: (1) find the URL for the picture, then (2) figure out how to insert it into your post.