How to configure mysql server?

[Timothy Murphy]

I'd like to run mysqld on my desktop "alfred"
and run a mysql client on my laptop "elizabeth".

It seems I need to grant permission on alfred
for tim at elizabeth to access the server,
but I have not found how to do this.

I'm running mysqld version 5.0.22 under Fedora-5.

When I try to set the password for user "root" on my desktop
I get the error:
------------------------------------------
[root at alfred tim]# mysqladmin -u root password whatever
mysqladmin: connect to server at 'localhost' failed
error: 'Access denied for user 'root'@'localhost' (using password: NO)'
------------------------------------------
Another attempt fails:
------------------------------------------
[root at alfred tim]#  mysql -h localhost -u root -p
Enter password:
ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using
password: YES)
------------------------------------------

Does this mean that "root" already has a password, which I do not know?

The only user I can login as is "mysql",
but then I can do little:
------------------------------------------
[tim at alfred ~]$ mysql -u sql -p
Enter password:
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 4 to server version: 5.0.22

Type 'help;' or '\h' for help. Type '\c' to clear the buffer.

mysql> grant all privileges on *.* to tim at elizabeth ;
ERROR 1045 (28000): Access denied for user ''@'localhost' (using password:
NO)
mysql> quit;
Bye
------------------------------------------

Could some kind guru tell me the solution to my quandary?

-- 
Timothy Murphy  
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland