NoelDP and mjm64 are correct. SURT is a self-installing utility that executes when you install it.
The checksur logs are located in C:\Windows\Logs\CBS - unlike the CBS log, you can edit them in place.
It leaves the cabinet files on your system in C:\Windows\checksur
When you install it, it creates a temporary file on your C: drive that contain the applications checksur and checksurlauncher. This directory is removed upon completion - you really don't need it. If you install / run it again - it will check for updates and download only what it needs (new core cabs).
And yes, you can install/run it multiple times, but you really only need it when you need it (you're having issues with core files not being fixed by SFC or Windows Update components need some help).
A more comprehensive solution to missing or corrupt system files is a Repair Install - you boot off your Windows install disc and select upgrade (it used to be called repair). The advantage this has over any utility running in windows is that since you booted from DVD or USB, the critical system files on your system hard drive are not locked. This means that the repair can manipulate any file it needs to correct.
When I'm having serious issues on my machine, I'll run SFC a few times (booting between), see what the last SFC log tells me (manually repair no more than a few files), run SURT once, and if necessary find my Windows DVD and run the repair install.
I've only had to re-install once or twice, and that was due to my own errors trying to fix the system in unorthodox ways.