Generally, how do you describe the functions of the basic parts in a buck or boost converter? The parts are enumerated in the post
I'm an applications engineer at Maxim Integrated (currently in merger with Analog Devices; competing with Texas Instruments). As a resource, there's a lot of technical papers (called applications notes or reference designs) which are directly published by IC manufacturers. Here's a place to start:

TUTORIALS 2031
DC TO DC BUCK CONVERTER TUTORIAL
https://www.maximintegrated.com/en/design/technical-documents/tutorials/2/2031.html
Abstract: Switching power supplies offer higher efficiency than traditional linear power supplies. They can step-up, step-down, and
invert. Some designs can isolate output voltage from the input. This
article outlines the different types of switching regulators used in
DC-DC conversion. It also reviews and compares the various control
techniques for these converters.


TUTORIALS 986
INPUT AND OUTPUT NOISE IN BUCK CONVERTERS EXPLAINED
https://www.maximintegrated.com/en/design/technical-documents/tutorials/9/986.html
Abstract: Input and output noise in buck (step-down) converters can concern the system designer. This application note provides a theoretical explanation of the individual contributions of conducted noise on the input and output sides of buck converters. These equations will allow the power-supply designer to optimize components for noise immunity.

We make and sell just the integrated circuit (chip) itself, but to actually solve the customer's problem requires some support circuitry and a deep understanding of the problem. So we publish Reference Designs (and Evaluation Kits) which are a kind of example, proof-of-concept that we use to show an example of a complete system. For switching power supplies in particular, there are subtle parasitic effects that are sensitive to the exact layout and components used. Replacing a torroidal power inductor with a choke inductor won't work. Trying to build a switch mode power supply on a solderless breadboard won't work. I've worked a number of customer service cases like that. We encourage our customers to just copy our working reference designs, including the PCB layout and the parts list (bill of materials), because those factors are important. Many of these application notes and reference designs include &quot;scope shots&quot; showing the actual waveforms one should expect to see on the switching nodes.
https://www.maximintegrated.com/en/products/power/power-reference-designs.html
https://www.maximintegrated.com/en/design/technical-documents/index.html/app-notes/products/power
https://www.maximintegrated.com/en/design/technical-documents/index.html/tutorials/products/power
And just giving equal time to the competition, Texas Instruments (ti.com) has a whole product line they call &quot;Simple Switcher&quot;, their SEO puts it pretty high on any web search list. From there you can specify the basic design requirements (VinMin, VinMax, Vout, Iout) and their machine provides a switcher design, complete with bill of materials -- they are partnered with the big distributors too, so a customer can just buy the whole solution without having to understand how the design works. A very neatly exectued marketing idea, I respect.
I'm always a bit put off by the whole &quot;explain the function of each part&quot; methodology, because it tends toward oversimplification (&quot;the diode only conducts one direction&quot;) and it overlooks how groups of components interact. I think for switch-mode power supplies in general, it's more useful to think in terms of the flow of energy through a charge loop and a discharge loop. When the switch is in one position, the current through the inductor L is increasing or &quot;ramping up&quot;, as energy is being stored into L. There is a practical limit to how much energy can be stored in a given inductor, that affects the switch on-time. Then, when the switch is in the other position, the current through the inductor begins decreasing or &quot;ramping down&quot;. This causes the inductor terminal voltage to change. The inductor voltage opposes changes in the inductor current, and the capacitor current opposes changes in the capaictor voltage. Also be sure to notice that the diode itself is really part of the switch; if you had a Maxwell's Demon you could replace SW1 and diode D with a doube-pole, single-throw switch; using the diode ensures that the LC current always has a path to flow, regardless of whether SW1 is conducting or not.
The inductor needs to be able to store a lot of energy in its magnetic field, so usually TDK drum cores are used (under different brand names like Sumida), and the wiring gague needs to be large enough to minimize resistance yet small enough to get a good number of turns.
The capacitor needs to be able to handle load transisent demand current, so its effective series resistance is important -- often cermaic capaictors are used on SMPS output. Not shown on the schematic is the input capacitor, which is usually aluminum-electrolytic to support high inrush current.
The diode needs to turn on rapidly because any interruption in the current flow will make the inductor arc... Schottky has low Vf. Often for higher efficiency we use a low-side MOSFET in parallel with the diode, but due to timing requirements the diode has to handle the initial turn on at the start of the inductor discharge cycle.