There are some very slick third party solutions for this problem, including Snapz Pro X and Screenflow, but you're right, Quicktime Player on your Mac system can do the job just fine, and if you've practiced and are prepared, the results can be quite professional!

The first thing I'll suggest you use is an external microphone to record your narration. You can use the built-in mic on your Apple computer, but generally those are low gain and have a lot of ambient background noise. Much better to use something like a Blue Microphone Snowflake or even a high-end Yeti Pro, which is what I used for this tutorial. Turns out audio is the most critical element in a good video, but that's another article...

To get started, think of exactly what you want to record, perhaps even writing out a rudimentary script, then launch the app in question and move it to a central spot on the screen. Now launch Quicktime Player and look at the "File" menu:

The selection you seek is "New Screen Recording...". Select it and you'll be presented with a small black control window:

You're not quite ready to click the red "record" button yet, though. Instead, click on the small downward pointing white triangle on the right edge to produce the settings menu:

Here's where you can ensure that it's selected the correct audio input device. You can see I have quite a few! For this, I need to pick "BLUE USB Audio 2.0", which I do.

Now I'm ready to record. A tap on the red square button on the control window doesn't start things, however, it gives me the option of specifying a region of the screen to record or the entire window:

Since I'm just going to demonstrate something on the iTunes player window while it's in "mini-player" mode, I'll select the region around the player as tightly as I can:

Once I've clicked and dragged to select the region, it resizes for the dimensions that Quicktime Player prefers, and produces a "Start Recording" button:

A click on it and I'm recording the audio and whatever shows up in that window region.

When I'm done, I move the cursor back to the control window and click on the record button again, which has changed from a red square to a black "stop" square.

The recorded video appears in a control window for me to review:

You can see that it's 0:20 or 20 seconds in duration. Perfect. Now to save it. I accomplish this by choosing "File" --> "Export to Web...":

And a bunch of options appear:

Everything looks good? Great. Click on "Export" to save your new screen recording to a file, along with a lot of helpful information from Quicktime on how to incorporate it into your own Web page. When it's done, you'll see this:

You can follow their directions on how to incorporate it into your page, but a quick click on your new desktop file and you'll see the video looks good and sounds great.

Surprisingly simple and the results are quite presentable!