Generally speaking, I alternate between 2 workouts & I know how many laps are in each set. As long as I make sure I get all my sets in I know how many laps I did. As far as counting during the set while I am swimming I find it easier to keep track by counting my yardage - each lap is 25 yards, so I count by 25's instead of by 1's (for each lap). It's an unusual occurrence for me to not get my sets in, so when I don't it stands out & I can keep track of what I didn't get done. Also, the majority of those few times I know going into it I'm going to have to cut it short due to time constraints, so I pre-plan what I'm going to cut out.....

There are lap counters to wear on your wrist but I don't use it. If you can, use the beads that divide the lanes. Move a bead for every set in your routine. You could move a bead for every 100M for example. Depending which workout I use determines whether I use the beads or not.

I do my swim in sets. Three laps of freestyle, three of breast and one butterfly and then I repeat it. That way I never have to count higher on laps than three and I just keep track of sets. I am up to five sets, but I am only at the beginning of that fifth set. When I started I could only do three sets.

Progress...

I use my timex tap watch, I put it in the chrono mode and tap after each lap so I don't have to stop. Also keeps track of my time/lap.

You can also purchase a Garmin Swim which keeps track of almost everything plus you can turn on the GPS to track open water swimming.

My friend has a swimovate poolmate watch that is really similar to the Garmin swim without the GPS. Is UK based.
My friend also had other tricks like using the alphabet instead of counting laps, each lap she would try to think of an object, insect etc that started with the next letter of the alphabet.

Or she also used pipe cleaner with beads on it, attached to her water bottle.

We are training for endurance and long distance so more continuous swims. I save my drills and sets for when go to my Masters swim and they keep track of that stuff for me, hehe.

Edited to add: I wish I had been able to find that finger click thing. I tried googling for options before I bought my watch and nothing came up

I use my water bottle and the tiles on the edge of the pool. Every time or two that I reach the end with the water bottle I move it one or two tiles from the edge of the lane. Each tile represents 50m so when I have done 10 tiles it is 500m and I change direction of moving the bottle. I generally swim 1, 1.5 or 2km so it is 2,3 or 4 sets of 10 tiles.

Very crafty.