There are various methods, however I will outline the steps by mounting a virtual DVD ISO (I used Cisco UCS Server - so my Virtual KVM was CIMC).
To mount the ISO and restarting the server and booting through the DVD, follow my other blog post (You would mount a different DVD image which would have the upgrade vSphere ISO).
Note: Check VMWare Compatibility to check if you can go from a specific source to a destination.
Here are the steps:
Once the DVD starts booting, the following screen would appear:
Note: Be careful in this step
Note: vSphere on your local desktop will have to go through an upgrade once the ESXi is upgraded.