After Install LAMP Server Locally on Ubuntu 9.10(Karmic), I consider to run wordpress locally on LAMP server with Ubuntu 9.10 Karmic Koala.

Setp 1: From http://LocalserverAddress/info.php

Apache Version 2.2.12, MySQL version 5.1.37 and PHP Version 5.2.10

have been confirmed. They are meet the requirements to run wordpress.

Ref:  minimum requirements to run WordPress

Step 2: Create a database for WordPress and an user who has all privileges for accessing.

Here, using the MySQL Client(if you use Using cPanel or Using phpMyAdmin, follow the instructions accordingly),

$ mysql -u root -p
mysql> CREATE DATABASE wordpress;
mysql> CREATE USER wpuser;
mysql> SET PASSWORD FOR wpuser = PASSWORS(“wppassword“);
mysql> GRANT ALL PRIVILEGES ON wordpress.* TO wpuser@localhost IDENTIFIED BY ‘wppassword’;
mysql> FLUSH PRIVILEGES;

Step 3: Download Wordpress from http://wordpress.org/download
$ sudo wget http://wordpress.org/latest.tar.gz
$ sudo tar -xzvf latest.tar.gz

Move the wordpress directory to the root directory of Apache web site, /var/www/,
in wordpress directory, rename the wp-config-sample.php file to wp-config.php.
$ sudo nano /var/www/wordpress/wp-config.php
Change putyourdbnamehere to wordpress.
Change usernamehere to wpuser.
Change yourpasswordhere to the wppassword.
By accessing http://LocalserverAddress/wordpress   or   http://LocalserverAddress/wordpress/wp-admin/install.php
to setup the wordpress configure page.

Ref: Installing WordPress Guide