What are you running it with? Are you using the startup script, or are you just running it from CLI?
Here is how you set it up (Assuming you installed the Slackware package that came with the distro):
1. su as user mysql (or log in as user mysql). It should already exist.
2. run the init script /usr/bin/mysql_install_db. The script should create administration tables it needs to be able to run inside the usr mysql. To verify this, cd to ~mysql and see if there are 2 directories: (1) mysql, (2)test. (You should only worry about having the mysql directory)
3. Now, there exists a startup script for mysql under /usr/share/mysql/ called mysql.server. You can use that script to start the mysql server daemon how ever you want to. To test that everything works and runs, just run it (as user mysql) with the start argument. If sucessfull, you should see something like this:
Starting mysqld daemon with databases from /var/lib/mysql
If you fail, check the log under ~mysql/<your_host_name>.err, or /var/lib/mysql/<your_host_name>.err (~mysql is a link to /var/lib/mysql), and see exactly what the error was.
Hopefully if you follow the above process, it should be able to run. Just remember that everything should be owned by user mysql, and run by user mysql.
GL
