First you'll have to configure an external blog, (do that here). Alternatively, you can find the blog set up by going to 'Your account' and selecting 'Your blogs', which takes you to the same place. You'll be guided through the set-up process and at the end you can try a test post to make sure everything works.
Once that's done, you can blog any public photo you see on Flickr. When you're looking at a single photo, for example, http://www.flickr.com/photo.gne?id=23754, you'll notice the "Blog This" button next to it.
If you don't see a "Blog This" button, you probably either need to make the photo public (to do that, click the word "private" that appears under the photo on your photos page and to the right of the photo on that photo's individual page), or you need to install Flash. You can check your Flash version here (make sure you have version 6 of higher). If you need to install Flash, it is a free download available from Macromedia.
Click the 'Blog This' button for the photo you want to post. Assuming you've set up your blog, you will be able to post straight away by adding a Title and Body for the post. There's a link to your blog as well so you can check that the entry looks OK.
You can set up as many blogs as you like.
You can also create your own Flickr moblog. When you upload a photo to Flickr via email, and you have at least one blog set up in Flickr, we can post your photo to your blog automatically. Check your settings here.
You can send photos straight from your phone to your blog via Flickr. You need to make sure you've set up your blog in Flickr first, and then you need to get yourself a special email address to send your photos to.
Each member of Flickr can get a specific 'Upload2Blog' email address for this - you can set yours up here. Once that's done, photos uploaded to the new address will be blogged automatically, as well as being posted into your Flickr photostream.
When you upload photos via email, use the subject line to give your photo a title, and the body of the email to give it a description. These will be carried over to your blog entry, if you specify this on the set up page above.
My mobile phone service provider puts a signature in all the posts I send from my phone! How do I stop that?
Unfortunately, you can't do anything to stop this automatically. We need to snip out each different sort of signature as they come up. There's a specific thread in FlickrBugs where you can report new ones, and we get to them as soon as we can.
In the meantime, you could choose not to include the body of your email in the post you make to Flickr (and your blog), or just delete the crud when you are editing in Flickr.