I have a mid 2009 MBP with Mavericks and am increasingly seeing the spinning wait cursor or spinning disc pointer - how do I try to troubleshoot what might be happening? Indeed, in what situations does this object appear - are the situations purely internal in the sense of lack of CPU power or RAM or motherboard characteristics, or can external factors also impact such as HDD or network characteristics? I presume that the spinner appears in response to the current application not to some background event, so, in troubleshooting I'd also presume you would need to look at logs of some sort of the current application and possibly of a general nature, things with which I'm not familiar.
One would use the Activity monitor in your Utility folder to find out the Loads to the CPU, RAM or Disk.
On my MBA 10.9.4 it looks like this: