Export your WordPress database from the old blog by following these instructions. Now, on the new server, use phpmyadmin to access the new blog's database and proceed to the "SQL" tab.
Now, search your database export for the titles of the single posts that you want to import, or look for the section called "wp_posts". You will find the desired post(s) in this format:
INSERT INTO wp_posts
) VALUES (4,1,'2004-10-04 22:29:43','2004-10-05 05:29:43','Blah Blah Blah. This is the post content. Boring, yes?','Post Title',0,'',NULL,NULL,'publish','open','open','','post-title','','','2004-10-04 22:29:43','2004-10-05 05:29:43','',0,'http://www.example.com/wordpress/archives/2004/10/04/post-title/',0);
Now, return to phpmyadmin and the SQL tab for your new blog's database. To insert the above post, copy all of it, starting at (and including) the post's
INSERT INTO query, and stopping before the next post's
INSERT INTO query. This will insert the post from the old blog into your new blog's wp_posts table. Once it is inserted, you will probably have to change the post's URL and ID number in order to avoid conflicts with other posts.
The above instructions are only for inserting select posts from an old blog to a new blog. To completely replace the new blog with the old blog, just replace the new blog's database with the old blog's database. To do that, follow the backup instructions posted above, and follow these instructions to restore the database.