Couple paths, one that is recommended is to replace your hardware. Get a new MCS servers for the install. If your servers are 2 years old, might as well. Its a shame to put all this time into an upgrade on old hardware, then turn around and do it again in a year or so when you have to upgrade again.
Anyways, I digress.
You can re-use your hardware if it meets the 6.x hardware standard. There are a few tools you can run on your CM 4.x box.
Run the Cisco Upgrade Assistant. You can find this in the CCO under CUCM. This will check your machine for hardware, etc
Next you will run the DMA process for 6.1 it will spit out a TAR file of your entire database and configuration.
Cross your fingers, load the 6.1 software. It will blow away your current server, then ask for the DMA file you have. (about 60-100 meg file) It will then import and configure your 6.x server for you with all your devices, partitions, etc.
Of course, there are a ton of other steps to follow, but feel free to ask other questions.
Having new pair of Publisher and Subscriber gives you the chance to test it in a lab enviroment, get the licensing worked out, check features, etc. Then it's simple to unplug the old 4.x servers (in order!) then bring up the new paird of 6.x (in order!).
These are the paths to get to each CCX logs through CLI. They may be helpful if you are having issues accessing RTMT or downloading logs through it.
If you want to download them you have to prefix "file get " and you can add one of the options (re...