Ah yes, snapping can be bit daunting for new Inkscapers. One good general rule, to start with, with snapping, is to have the control bar set up specifically for each situation. In some tools/features, people will find a particular configuration that works for them, and stick with it. But with snapping, it's important not to have too many snap targets (or else whatever you're dragging will try to snap to everything). Here's how to set up for my suggestions. Note that if you hover your mouse over a button, some little text will appear, which describes what that button does. So set these 4 buttons engaged, and all the others not.
1 - Enable snapping (top or left button, depending on how you have your window set up)
2 - Snap nodes or handles
3 - Snap to cusp nodes
4 - Snap to smooth nodes
You'll know that the snap was successful when you see the tiny text on the canvas, that tells you which element snapped to which target. In a simple drawing like this, it's not as helpful as it would be in a more complex drawing.
This reminds me, I've been meaning to write a newbies' guide to snapping. I should do that soon

Anyway, another problem, that perhaps is a little less common, is how you set the snap strength. And having that in Document Properties is a little frustrating. But that really is the best place for it, imo. Actually I call it snap "strength" because that how it seems to effect the physical "snap" on the canvas, to me. But it's really called snap distance. Until you have more experience with Inkscape, perhaps it would be better to have them all set to "Always Snap". And simple drawings, that may be all that's needed. But if you start to work in more complex drawings the snap distance can become important. At least that's my experience. And there are some more snap controls in Inskcape Preferences. But again, for new users, the defaults are probably just fine

After re-reading the last paragraph of my suggestion, I'm not sure how I could make them more clear. You just have to do one step at a time. Unfortunately, I haven't had much free time lately, so I can't really draw up a diagram right now. But if anyone else is game to make a diagram of my suggestion, I won't mind at all.
