You need to make sure that mod_userdir is loaded and enabled. The following commands turn it on in my Debian-packaged version of Apache. This should work fine for OpenSUSE, although you might need to adjust the path to the module in the LoadModule directive. The command might already be in your httpd.conf but just commented out. At a minimum you will need LoadModule and the first UserDir directive, although the second one to prevent root from using that directory is probably a good idea.
LoadModule userdir_module /usr/lib/apache2/modules/mod_userdir.so
<IfModule mod_userdir.c>
UserDir public_html
UserDir disabled root
<Directory /home/*/public_html>
AllowOverride FileInfo AuthConfig Limit Indexes
Options MultiViews Indexes SymLinksIfOwnerMatch IncludesNoExec
<Limit GET POST OPTIONS>
Order allow,deny
Allow from all
</Limit>
<LimitExcept GET POST OPTIONS>
Order deny,allow
Deny from all
</LimitExcept>
</Directory>
</IfModule>