For me and my experiences it was usually just using a standard issue note book that was simple hand written records of events. The more modern equivalent would likely be a simple word document or even a basic spread sheet based design with columns for the common items like the persons name, time, job or work order description, possible referance material, and general notes about what ever.
But unfortunately computer based stuff can be faked. A well worn and long used notebook carries far more credibility.
But its does not have to be complicated by any means.
My referance day was a bit exaggerated though. The names where changed and the forklift guy actually survived just fine. But he did actually drop the front tires off a loading dock because of bad brakes that went unfixed for far too long due to simple negligence on the large part of a warehouse managers lazy attitude and disregard for reporting general maintenance related issues.
A second forklift just lifted it back up from outside and pushed it back. No harm and no problems but someones butt got severely chewed though. It wasn't mine! I was the new guy at the time. I had not even been trained in on driving the forklifts.
But it was the place where I got fired in a poorly planed attempt by my own manager to hide his major screw up.
former coworkers I talked with afterwords said that the day I was fired was the same day that the log book disappeared off the chain. Which raised a lot of questions with everyone. Especially being that it disappeared after I was let go that day and I no longer had access to the building.
Plus it was well known by the others that I had written a considerable number of entries relating to how I had been cluelessly doing his work for some time and I had thus been writing it down as regular work related log entries like a good little worker was supposed too.
What drew the most attention as I understood it was that the accusations for my firing made absolutely no sense from the companies upper level views. I was accused of doing things wrong that where my managers work and not a lowly junior maintenance workers duties.
Sure I did them and wrongly at times too, but I was a 20 year old inexperienced kid who just happily took on what ever work I was handed. I never knew I was doing much of my mangers job without proper clearances and training.
I just thought that I being given more work since I showed myself to be efficient and responsible. It turned out I was doing a large part of his job while he didn't do much of anything.
Thats where the blaming me issue pointed to it being basically impossible for me to have ever done what I was accused of without his knowing it. The only way I could have been doing the things in question was if he was the one who had shown me how to do them in the first place!
Still it almost makes me sick to think of what I was unknowingly indirectly in charge of at that time and what I was doing wrong and how much worse things could have went because of it when I was there. Years later I still am not sure I would be all that comfortable with having that level of responsibility.
If someone had told me back then what I was doing and what it related to over all I probably would have broke down and cried right on the spot and probably had thrown up as well!
Ever since any work I did for any business has always had some from of log book of my own along with the normal company paperwork as well.
A simple hand written notebook with a few daily entries about what you did and who did what plus general time line references that link to company paperwork will go a long way if you ever have to use it. You never know when you may find out your doing someone else's job and will need proof that you where mislead into doing it!
I hope this gives you some idea of how useful and serious a simple notebook could be.