One problem you will find is that many service providers will only support the connection software package that they distribute to new accounts. This is (typically) for Microsoft Windows :-( - and many service provider help desks seem to know nothing about Unix (or Linux). So, be prepared for limited assistance from them!
You could of course do the individual a favour and educate then about Linux (any ISP help desk person should be reasonably 'with it' in Internet terms and that means they should have a home Linux box - of course it does)!
OK - your PPP connection is up and running and you can ping the PPP server by IP number (the second or "remote" IP number shown by ifconfig ppp0), but you can't reach anything beyond this.
First of all, try pinging the IP numbers you have specified in /etc/resolv.conf as name servers. If this works, you can see beyond your PPP server (unless this has the same IP number as the "remote" IP number of your connection). So now try pinging the full Internet name of your service provider - eg
If this does NOT work, you have a problem with the name resolution. This is probably because of a typo in your /etc/resolv.conf file. Check this carefully against the information you acquired by ringing your service provider. If all looks OK, ring your service provider and check that you wrote down the IP numbers correctly.
If it STILL doesn't work (and your service provider confirms that his name servers are up and running), you have a problem somewhere else - and I suggest you check carefully through your Linux installation (looking particularly for file permissions).
If you STILL can't ping your service provider's IP name servers by IP number, either they are down (give them a voice call and check) or there is a routing problem at your service provider's end. Again, ring them and check this out.
One possibility is that the "remote end" is a Linux PPP server where the IP forwarding option has not been specified in the kernel!
A good general test is to try connecting to your service provider using the software that most supply for (gulp) Microsoft Windows. If everything works from another operating system to exactly the same account, then the problem is with your Linux system and NOT your service provider.