Jayce,
Kilted_John has provided the answer, but hopefully a few pictures will help... (Note: these instructions are specific to Flickr, anyone using an alternative picture hosting service can work out how to manage that one for themselves

)
First find the picture you want to use and click on it. You should now be looking at a page like this:
Image in photostream by
milfmog, on Flickr
Click on "Share this" (circled above) and a menu will open like this:
Share this options by
milfmog, on Flickr
Select "Grab the HTML/BBCode" (circled above) and the menu will change to this:
Select code type and thumbnail size by
milfmog, on Flickr
Select "BBCode" (circled above).
Select the size of thumbnail you require from the drop down menu (arrowed above). I have used the default medium size for these images.
Click on the box full of geek speak (just above the image size selector) to highlight all the text in it (if necessary you can click in the box then press Ctrl and A together to highlight all of the text).
Now press the Ctrl and C keys together. This will copy all the gibberish to your clipboard.
Go to your post and click where you want the image to appear, then press the Ctrl and V keys together to paste the code into your post, the copied code will look like this (without the blue box):
Code: Select all
[url=http://www.flickr.com/photos/27333144@N04/4911315554/][img]http://farm5.static.flickr.com/4098/4911315554_b6f99930e5.jpg[/img][/url]
[url=http://www.flickr.com/photos/27333144@N04/4911315554/]Rainbow (6)[/url] by [url=http://www.flickr.com/people/27333144@N04/]milfmog[/url], on Flickr
If you now preview your post you will see the image; clicking on the image will take the reader to the page you were on when you selected "Share this" and the reader can select other sizes to view if they are available and navigate any public images in your photostream.
Below your picture you will see the name of the file and your Flickr name. Clicking these take the viewer to the image or your Flickr profile respectively. The code is structured as below:

The section between the first url code marker and /url code marker produces the picture as a clickable link.

The section between the second url code marker and /url code marker produces the title of the file as a clickable link to the same Flickr screen as clicking on the picture. This is useful if you do not want to add the picture within the post (to keep page loads fast for readers) but want people to be able to see your picture if they want to.

The section between the third url code marker and /url code marker produces your Flickr name as a clickable link to your Flickr profile page.
If you do not want any one or two of these options, simply delete the appropriate parts of the BBCode as detailed above. (Remember to remove the square brackets containing the URL markers for the section you delete.) I usually use just the first part of the code and delete sections two and three. I left all three codes in for this post so that you would see the most complete option.
NOTE: If you have marked the image as "Restricted" or "Private" it will be displayed in your post, but nobody will be able to access it within Flickr unless they log in to establish their age (Restricted pictures) and that that are authorised to view it (Private pictures).
Give it a whirl and see how you get on.
Have fun,
Ian.
Edited to clarify text slightly and add the note about Restricted and Private images. - Ian.