How do they work? Quite well, thank you, and quietly

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Hydraulic lifters are used, because valve stems grow (expand in length) as things heat up.
When an hydraulic lifter is installed, the spring inside makes the lifter expand (it telescopes, like a slide trombone) to eliminate any gap in the valve train. You've already seen this, in the old lifter you took apart.
Fill the lifter with oil (between the lifter's body and the plunger inside), so that the lifter won't just squash again when the cam comes around. The lifter acts as if it were solid, because it's full of oil. No gaps in the valve train, so no tick-tick-tick, and it acts like a perfectly-adjusted solid lifter.
Great, but what happens as the engine warms up, and valve stems lengthen due to the temperature increase? Well, the lifter is designed with a very small leakage between body and plunger, so that the lifter can collaspe slightly, over a length of time , as the valve lengthens.
The action is very similar to that of a shock absorber. If you try to squash a shock absorber suddenly, it just ain't gonna happen - it's solid as a rock. But if you take a few seconds and squash it gradually, it's pretty easy.
Likewise, when the cam comes around and suddenly pushes on a valve lifter, the lifter doesn't have any time to squash (collaspe) - so it stays solid, and transmits (practically) all of the motion to the valve train. On the other hand, as the valvetrain expands gradually (due to temperature), the lifter has plenty of time to shrink itself a bit (via gradual leakage)and compensate.
Basically, hydraulic lifters have the ability to take up slack, stay solid when acted upon suddenly, and shrink gradually when acted upon over time. "It's a rate thing." The rest is just details.
BTW, I think the pushrod gets its supply of oil mostly from the oil pump, to the lifter body, to the plunger and up the pushrod - but I don't think the cam pushing on the lifter has much to to do with pushing oil up the pushrod. There's a ball check valve in the base of the plunger, so I think very little (if any) oil actually would be pumped up by the cam action.
"Another Stu novel
" Sorry - but that's my story. Hope it gives someone a lift
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[This message has been edited by StuGood (edited 10-05-2003).]