I just installed SUSE with MySQL.

./mysql start

Did that and it started the service.

db1:/var/lib/mysql # mysqld_safe &
[7] 10240
db1:/var/lib/mysql # Starting mysqld daemon with databases from /var/lib/mysql

Then I do:

mysql -u root -p

I get:

ERROR 2002 (HY000): Can't connect to local MySQL server through socket '/tmp/mysql.sock' (111)