As normal users can't use wvdial to dial a ppp conection by default, you need to change some permissions:
chmod +s /usr/bin/wvdial chmod +xs /usr/sbin/pppd
Also make sure that the following files are readable by user:
/etc/resolv.conf /etc/ppp/options /etc/ppp/resolv.conf /etc/ppp/peers/wvdial
For example to set /etc/resolv.conf readable to all users:
chmod a+r /etc/resolv.conf
Another way to do this, in a more controlled enviroment is to set up a group called dial or dialout and give this group the above permissions and set the above files with this group(s).
If you can't access the Internet through your dialed connection as user, backup your /etc/resolv.conf and make it a symlink to /etc/ppp/resolv.conf.