SephStorm, it's all about getting as much information as you can.
Sometimes there is an available privilege escalation exploit, other times you have to really stalk it.
What I tend to do is have a look at all of the processes, see what is running with more privileges than me and if there are any ways of interacting with that service to get code execution.
Offensive Security's Pentesting With Backtrack is a great course that gets you really thinking about all of this, finding out this for every piece of software and configuration file takes a long time and you get really desperate, and all you get is 'Try Harder!'
I would recommend the course if you really like a challenge and the skills you learn alone are worth the price of the course

~TheXero