I keep a spreadsheet log on an iPad and update it after every range session. I keep track of firearm by caliber and rounds by ammo brand/type. I also record the number of rounds I shoot myself, my wife, or guest.
I set up a data entry page, then have a summary page that reads the input and calculates totals by weapon and caliber, as well a totals rounds by caliber by individual. I recently set up a summary that shows me the rounds shot each month by caliber to help me estimate my purchase goals (this has really been thrown off since the beginning of the year).
I don't claim perfect counts, but they are
pretty close. I know this kind of record keeping is not for everyone, but I find it useful for myself.
By the way, one thing I haven't kept track of is the number of dry firings on each firearm. I'm too far down the path for meaningful numbers even if I started tracking this now, so I probably won't bother with it.