In the PM you receive it should link to the tournament you are invited to; all you then need to do is click the sign up button (link) on the page.
I guess you could expand the PM text a little to say something like below by editing the
notify_tournament_invite_message phrase.
Code:
{1} has invited you to participate in an arcade tournament.
Game: {2}
Tournament Title: {3}
You can review details of the tournament through the link below and register your participation by clicking on the 'Sign Up To this Tournament' link. If you don't wish to participate just ignore this message.
['url={4}/arcadetourmnt.php?do=viewtourmnt&tid={5}]View Tournament Details[/url]
['url={4}/arcadetourmnt.php?do=jointourmnt&&tid={5}]Sign Up To This Tournament[/url]
You will need to remove the ' from the coded lines as it is only included to allow the code to show)
['url={4}/arcadetourmnt.php?do=viewtourmnt&tid={5}]View Tournament Details[/url]
['url={4}/arcadetourmnt.php?do=jointourmnt&&tid={5}]Join This Tournament[/url]