It depends somewhat on which method you're using to make the sauce. I also find softened whole butter a bit trickier to work with in turning a sabayon into a hollandaise, bearnaise, or the like, because the emulsion is less stable.
Beyond that, clarifying butter separates butter into three components: a foam you skim and remove, clear butterfat, and waxy milk solids. Adding the milk solids will thin the sauce, where adding the fat will thicken it. I have found it easiest to add butterfat, and if the sauce gets too thick whisk in a little milk solids to thin it a tad.
There are three basic methods for making a Hollandaise-type sauce: blender, bowl over hot water, sloped pan over direct heat.
Blender: foolproof, lots of cleanup, somewhat unrefined sauce with minimal possible variation. I believe Julia Child is credited with inventing this method.
Slope-sided pan over direct heat: slightly tricky, very quick, no mess, immense variation possible to match your whims. If you want to learn, learn this way.
Bowl over hot water: tricky, rather slow, some mess, some variation possible, pain in the rump. I have no idea why anyone ever uses this method.
To learn the blender method, read Julia Child. I believe most of her cookbooks have this in them somewhere.
To learn the pan method, read James Peterson, Sauces.
Don't learn the bowl method.
The quick-and-dirty of the pan method:
Put 1 Tb cold water per egg yolk in a slope-sided or curved pan. Your first time out, I suggest that you use 3 egg yolks (and thus 3 Tb cold water). Clarify 2-3 sticks of butter: melt gently over medium heat, remove from heat and skim all floating foam, ladle clear butterfat into a warm bowl leaving the milk solids behind. Have on hand 1/4 lemon, salt, cayenne (optional), and white pepper (optional). Get a good whisk.
Whisk the yolks and water fast for about 30 seconds until foamy. Place pan over medium heat and whisk steadily for about a minute. Around that time, give or take, the mixture will quite suddenly turn very pale, roughly double in volume, and thicken to the point that you can see the bottom of the pan clearly between whisk strokes. Now whisk fast for twenty seconds -- I count under my breath, personally -- during which time the yolks will come up significantly over 160 F, killing any salmonella. Remove from heat and whisk rapidly for another 20 seconds, so it won't cook any more when you stop whisking. (You have now made a classic sabayon.)
Now beat in the clarified butter exactly the way you did with your mayonnaise. There's no need to be super-slow and careful about it: the emulsion is quite stable, and you're adding pure fat, so it will not break especially readily. As the emulsion builds, i.e. as you add more fat, you can add it more and more rapidly if you choose. Ideally, you want to add it a bit on the quick side, because that way you don't lose all the air, but this is a minor refinement, not something to worry about the first time out.
Once the sauce is as thick as you'd like it to be, squeeze in much less lemon than you'd think, add a pinch of salt, and if you wish add a small dash of cayenne and/or white pepper. Stir to mix, then taste. The lemon flavor should not be strong, just a citrus accent to the clean, buttery taste. The pepper(s) are just there to help the flavor get past the richness, and should not be identifiable on their own.
Congratulations: you have now made sauce Hollandaise.
Last note. The underlined bit above is the most important part. Once you see it happen, you'll know: it's remarkable. Every time I've seen someone screw up making the sauce this way, one of two things has happened: either the person hasn't really whisked steadily, taking little breaks and stuff here and there, resulting in scrambled eggs; or the person has been so worried about scrambling the eggs that the sauce has been pulled off the heat before it had thickened. The latter problem seems to be very common, and is serious, because (a) the sauce doesn't ever thicken properly, (b) the emulsion is unstable, so the sauce is liable to break, and (c) you never really cook the eggs, which worries a lot of people with some justification. Just trust your eye: if the sauce is very pale and quite thick all of a sudden, start whisking faster for another 20 seconds and then pull it.
It's not hard to learn, and it's very satisfying when you do.