The first link has more detailed information about moving blogs to your own domain, etc. but I'm usually interested in moving the blog between WordPress.com addresses (e.g. going from example1.wordpress.com address to example2.wordpress.com), so here are the instructions (from the second link):
Instructions for Changing Your Blog Address
- Go to My Blogs in your dashboard and move your mouse over the address of the blog you wish to rename. You will see that a change blog address option appears. Note that you will only see this option for blogs that you own.
- Click the change blog address option for the blog that you wish to rename.
- A screen with some confirmation text and fields will appear. Read the information presented on this page very carefully. Most importantly, make sure this is the action you wish to take.
- Enter the new name for the blog in the first two import fields. Verify that this new name is what you want it to be.
- Next, you will be offered the opportunity to register a matching username (the name you use to login) and have two options if you decide to do so:
- You can choose to change your current username. If you choose this option, you will not be able to revert back to the original username, and it can affect profile URLs for other services such as Gravatar or IntenseDebate. See Changing Your Username for more information.
- You can register a separate account. You will need a separate email address to do this. If you create an additional username, both your current account and the new account will be added as administrators to the blog.
- The final option presented on this screen allows you to discard your current address. This option will permanently disable the address and you will not be able to reuse it. Only select this option if you are sure you will not use the address again. If you want to redirect traffic to the new blog, you can keep the address and purchase the Site Redirect upgrade. [Update: Instead of purchasing the redirect, I usually choose the keep my old blog name and make a single post like "This blog has moved to mynewblog.wordpress.com"]
- Once you have completed the form, click continue anmynewaddressyou will be prompted with a summary of the changes you requested. Review this page and continue to change your address.Once you’ve completed all of the steps above, your blog will be rocking a brand new WordPress.com address.