When to turn base at towered airport?
You have a few questions here.


  ...downwind pattern and I hear something like this: "123X, tower, you are #2 for runway 3, following a Cessna on final." 


In this case what you will do is continue your down wind leg while scanning for the Cessna traffic, some towers may ask you to "report traffic in sight" in which case you will say "traffic in sight" when you can see the Cessna. If he is on a long final you can begin turning your base (assuming you are in a similar small plane of a similar speed) when he is on your beam (right off your wing tip). This should provide adequate spacing for you to come in properly. Keep in mind that the tower may also instruct you to do things to keep separation like "123X Extend your down wind 1 mile" etc.  


  ...instructed to make "left pattern for runway 3," am I supposed to wait for the base leg turn until tower clears me for landing?


This depends on where you are coming in from. I have flown into towered airports on the runway heading and simply come into the pattern on final and was cleared to land about a mile from the runway. Other wise I typically report my midfield downwind to the tower "Piper 12345 Reporting Left Midfield Downwind for RW24" then the tower will respond with my landing clearance or instructions to extend. While it is the towers responsibility to clear you for landing and what not, controllers are not perfect, you can continue on towards the runway in your pattern but if you have not been cleared you should go-around or ask for clearance. 

The other situation I have been in is a case where the controller deliberately does not clear you but has  you come into the pattern and approach. This occurred while they were waiting for an IRF plan to come through for one of the regional jets waiting for departure. Since they did not know when it would come in I was instructed to continue my pattern and would be cleared on final if they did not need to get the jet out. However I was explicitly told I would be cleared on final so I knew what to listen for.