How to upgrade SQL Server 2008 to SQL Server 2014 servers with mirroring configured We have two SQL Server 2008 R2 instances with mirroring configured. We want to upgrade them to SQL server 2014. 

How will this upgrade effect the mirroring between the servers, and also how should I proceed with this upgrade without causing an outage? 

As per my research I can upgrade the mirrored server first to 2014 and then do a failover on 2008 server to make it mirror and the 2014 as principal and follow the same procedure to upgrade 2008 as well. Could some one please shed more light to it. What are some intrinsic points that I need to take care of?
Your research is correct you have to first apply service pack on mirror instance and then failover the mirroring so as to make this mirror instance as primary. Now you have to apply patch on instance which is nor mirror(which was previously primary). I have done it many times and I do not see much Gotchas.


  and also how should I proceed with this upgrade without causing an outage?


There will always be an outage you just cannot avoid it, when you failover SQL Server have to be stopped on current instance and failed over and started on other so you can see outage is just unavoidable.

For your reference


Minimizing downtime when patching instance which is mirrored
Upgrade Mirrored instance
Steps to Apply a Service Pack or Patch to Mirrored SQL Server Databases


Start reading the first 2 articles and then the third one has step by step method with screenshots. 

The high level steps would be


Remove the witness server from mirroring(if you hjave configured witness)
Apply the service pack to the mirror server
Failover the mirrored databases over to make it principal
Apply the service pack to the former principle server (which is now a mirror)
Apply the service pack to the witness server
Add the witness server back to the mirroring configuration