The trick to a good hollandaise is that you need no distractions, and preferably three hands. When conditions are perfect, it's a two person sauce. One person to make the sauce, and one to run interference with the phone, other distractions (like children), and to get the butter out of the fridge at the critical moment. It can be done by one person, but two just makes things easier.
4 egg yolks
2 Tbsp. Lemon Juice
A stick of cold butter (1/2 cup)
A small saucepan
A mixing spoon (not a whisk)
I like to put the egg yolks and the lemon juice together in the pan, before ever putting the pan on the stove. Stir 'em together real good, so you have a solid bright yellow sauce. Now, before you turn on your stove, is the last time for about 20 minutes you can do anything other than stir this sauce, so get your affairs in order. If need be, the saucepan can be left on your counter like this for 10-15 minutes (see picture).
Phone off? Pets and children locked up? (These things can also be handled by your third hand.)
Okay. Turn on your burner to the lowest possible setting, put half of your cold stick of butter (1/4 cup) into the egg yolk mixture (leave the other half in the fridge), and then place your saucepan over the low low heat. Start stirring. Constantly. Not fast, but constantly. I like to use my spoon to swirl the half stick of butter around (see picture). Keep stirring until the butter is completely melted. The second it is melted, add the other half of the stick of butter, preferably, using your third hand, so the stirring NEVER stops. Keep stirring.
If it ever looks like you might be getting a curd (pretty much, you accidentally made a bit of scrambled egg), just take your saucepan off the heat, and continue to stir until the curds reincorporate into the sauce, or if they are big curds, you stop getting more, and then return the pan to the low heat to continue to thicken. Your sauce got a bit too hot for a second. It happens to the best of us. If you catch it early (you see almost streaks in the sauce), you can recover, and you won't see curds in the final sauce. If you get big curds, don't worry too much, the sauce will still be delicious, just will have some lumps, and won't be too pretty.
Stir the sauce until the second half of the butter is melted. And then, keep stirring. When the sauce is done, it will become ever so slightly lighter, but if you're not that good at determining color, here's another way to check it: Unfinished sauce is the consistency of milk. Finished sauce is like a thin pancake batter (see picture).
It's great on asparagus, chicken, fish, and artichokes.
Now, if you want to make Bearnaise sauce, it's the same thing, just add 1 Tablespoon White Wine (or white wine vinegar) in with the lemon juice, and at the end, add 1/2 tsp. dried tarragon, 1/2 tsp. dried chervil, and a 1/2 tsp. onion powder. Bearnaise is amazing on red meat.