Put about half an inch of water in a pan, bring to simmer, not boil. Never let the water boil while making the sauce, and make sure water doesn't touch the bowl that will contain the butter. (IOW, you don't need an official double boiler to do this.)
Melt some butter in another sauce pan or butter melter. You could even use a mixture of butter and olive oil. Jooolia will say to take off the melted butter from the solids; I don't bother.
Joolia incorporates a horrendous amount of butter into one egg yolk, but I don't put so much. I think it's less likely to separate when there's less butter in the sauce, and less butter or butter/oil means its not quite as rich.
Maybe about 4 tablespoons of butter or butter/oil, half a stick, to use with one egg or egg yolk. Get the butter hot but not smoking.
While waiting for water to simmer and butter to melt., crack an egg into a bowl that fits into the saucepan with the water, but doesn't touch the simmering water.
Use either the whole egg or just the yolk. For the 'cholesterol challenged' use the whole egg. Whisk it. Squeeze some lemon juice into the egg, to taste, salt if you like, whisk, add a pat of unmelted butter.
Put this mixture over the simmering water and let it heat while whisking. When the egg mixture is warm, but not turned to custard, and the unmelted butter has melted, start adding the melted butter or butter/oil slowly, while whisking. (Joolia will say butter added in tiny quantities drop by drop, but I add it faster, maybe it works because I don't use the amount of butter she does.)
Whisk and whisk, and let the whole mixture heat up until you can see it thicken, but don't let it over heat or the whole mess will separate.
Anytime it seems to be ready to separate, add some cold butter and whisk.
If you want to thin it out so it won't be quite as rich, add some half and half, maybe a couple of tablespoons. I think the name for this, or maybe if you add whipped cream to the hollandaise, is sauce mousseline. Whipped heavy cream added to hollandaise is to die for!.....and it just might kill you. LOL.