I've just started learning a bit of kdenlive and I'm trying to apply some effects (note: not transitions) to a clip that I've recorded.

The clip is pretty simple, is just a random recording of my desktop. The effect I want to apply is obscure to hide some personal information from the video.
I'd like to cover a certain rectangular region between time X and Y and then obscure a different region from time Z and time W, say.
How do I do that?

I have added the effect by right clicking on the click, I'm able to change size and position of the rectangle on the screen but I'm completely unable to specify the start and end timinigs for the effect. The effect is applied to the whole clip.

I know that when using transitions you can add keyframes, and I've seen some tutorials using this to make simple animations with images, but how to apply this to effects instead?

Is the only alternative to split the clip into multiple clips and apply the effect to the different parts separately?
What is the most practical way to take any effect and specify when it should start and when it should end?

First, not all effects support keyframes. You'll notice if an effect supports keyframes either because the effect's properties show either a "timeline" with keyframe markers or a button with a stop watch.

Now, when an effect does not support keyframes then, yes, you'll need to cut your timeline clip at the beginning and end of the region you want to apply the effect to.

In most cases this won't be of any concern unless you happen to have big effect stacks and some of them with keyframes spread across the whole original clip. But then, since around Kdenlive 15.12.0 we now have bin clip effects and we still have track effects that help with complex effect stacks. Alas, in your case simply cut your clip (Shift+R), slap on the effect to only this region, and you're set.

Did you know that you can copy and paste only the effects from one timeline clip to another? Very useful...!