You can list these categories below your name on the scorecard, and for fairways and greens just check off the box on any hole where you're successful (fairways hit means your ball is in the fairway on your tee shot; greens in regulation, or GIR, means your ball is on the putting surface in one shot on a par-3, two shots on a par-4, or three shots on a par-5). Putts taken per hole is just a counting stat, so count up your putts on each hole. (Note: As per the PGA Tour norm, only balls on the putting surface count as putts; if your ball is just off the putting surface, in the fringe, and you use your putter, it doesn't count as a putt for stats purposes.)
Two other stats we like to track are sand saves and strokes taken from 100 yards and in. A sand save is recorded when you get up-and-down out of a bunker (meaning one shot to get out of the bunker, then one putt to get in the hole). Your score on the hole doesn't matter. Even if you get a 9 on the hole, if your last two strokes represented getting up-and-down from a bunker, check off a sand save.
We didn't fill in the 100-or-less row in our example above, but like putts, it's simply a counting stat. Add up your strokes played once you've gotten inside 100 yards of the green.