Firstly you are going to be need to make sure that your images are uploaded to Flickr! ;-)
Then you need to go onto the image you want to show people (Go onto your Photostream and click on the image to load it up so that it looks like the view below) and click on the "more ways to share" button (as highlighted below)
This will open up the white tab shown above, where you can share your pictures straight to a variety of websites; you however need the BBCode for your image. To get it click on "Grab the HTML/BBCode" link as shown here
Then make sure that you choose BBCode from the options (This is really important!! Don't forget to do this!)
From the drop down menu you can choose the size you want to display the picture at (500 is a happy medium if you are unsure), then simply copy and paste the code (shown at arrow 2) that Flickr has made for you into your post! ^-^
The BBCode for the above picture is this...
[url=http://www.flickr.com/photos/manadh/8872404606/]What's this? // 28 05 13[/url] by [url=http://www.flickr.com/people/manadh/]Manadh[/url], on Flickr
...and this is all you will see in your post until you press Submit or Preview.