When troubleshooting SharePoint issues, the best way to filter out all the noise from your log files and sort it for easier troubleshooting is to use the ULS Log viewer tool.
Refer to my blog post on the ULS Log viewer comparison and verdict to get a feel for the other options and see how I got to my conclusion there. http://www.jeremytaylor.net/2012/07/14/sharepoint-uls-log-viewer-tool-comparison-and-verdict/
However, this ULS Log viewer tool does not display logs from other servers in the SharePoint farm, unless obviously its a single server farm.
The way to help you with a multiserver farm is to run the Merge-SPLogFile command in the SharePoint management shell. This command “merges” all logs from other servers in the farm and combines them into one ULS log file on the local server. That file can then be opened in your favourite ULS log viewer for troubleshooting.
Note: this works in both SharePoint 2013 and SharePoint 2010.
So how do we use it?
Here is an example of how I use it to grab all logs between say 10AM and 10:30AM on the 23rd July 2013:
Merge-SPLogFile -Path "D:\Temp\MergedLog-20130723-1000-1030.log" -StartTime "23/07/2013 10:00:00" -EndTime "23/07/2013 10:30:00"
If I know the correlation ID, then I would recommend you run the following command after updating it to your correlation ID:
Merge-SPLogFile -Path D:\Temp\MergedLog-419ac99c-81b2-0077-378d-3c23767d2955.log -Correlation 419ac99c-81b2-0077-378d-3c23767d2955
There are a lot more examples of what you can do with Merge-SPLogFile you can get by typing this in the SharePoint management shell:
Get-help Merge-SPLogFile -examples