Let's consider a scenario like below: 

A small web blog build based on LAMP stack and deployed on a shared hosting.
Suddenly it becomes popular in one day and it gets million hits per day. 
Since the developer have not consider high traffic, it caused server downtime and crashes. 

What would be a quick fix for such a scenario?

BTW I know on cloud Servers I may be able to add more RAM or CPU to avoid that like in Amazon EC2.