Notebook. I prefer traditional pen and paper.
Document it like so:
DL: Warmup, weightxreps, weightxreps, weightxreps | Reverse Band DL: Weightxreps, weight x reps, etc | Pullthroughs: sets x reps (ex. 5X15), abs, calves.
Fasted morning cardio: 25 mins.
That's pretty much an entry out of my log. I also like to record of I have a really off-day so I can look back at what I did before then to see where I fucked up. Similarly I like to record when I'm kicking ass and taking names. I use a highlighter and use normal yellow for kicking ass and orange for getting my ass kicked (I'm a visual learner, my notes for classes look like a fucking coloring book but I can distinguish one thought from the next at a glance).
I don't take it with me to the gym because I don't document weights for anything but main lifts and supplemental lifts. I don't record weights for accessory shit (does it really matter if I did 5 more lbs this week on triceps pushdowns? Fuck no).