Lots of ways to do this, but if it's important to have access to the old info, then you may consider doing what I already suggested, but in addition:
1. Make a copy of your wp source code and rename it something else. For example, assuming your blog is in a subdirectory called blog, then copy it and rename it blog1 or anything you want to name it.
2. Leave the config file in the copy the same as the original...change the table prefix back to the original if you have already changed it for the new site.
3. Dump the original tables in the db into an sql file, open it with a text editor, do a search/replace on the url to change the directory name from the old (http://yoursite/blog) to (http://yoursite/blog1) and then drop those tables in the db and import the sql file.
To see how to dump the db, make the changes, and import it back, watch the video below and just see the part about dumping/editing/importing the db...remember, you are only dumping the original tables...not the new ones of you have already set-up a new blog.
http://educhalk.org/blog/?p=82
Or, you could go about this the other way if you don't mind your main url changing and you wouldn't need to make any changes to the db. For example,
1. Make a copy of your wp source code. For example, if you current site is in a directory called blog, then copy that entire directory and call it something different...blog1 for example.
2. Open the wp-config.php file (in your new blog -- blog1) and change the table prefix to something different...say from wp_ to wp1_
3. Visit the new site and you will be prompted to install the new blog.
4. Post a link on the original site to the new site.
Again, lots of ways to do this...just something to think about.