This is a pretty simple how-to, because a doorbell is a pretty simple mechanism! The difficult part is in understanding music note blocks.
First of all, here's what a finished, two-tone doorbell looks like:
That's seriously all there is to it. There's a button outside your house that looks like this:
And, when pressed, it sounds a two-toned ring.
The real trick in this technique is the timing and the tones, so that's what I'll talk about.
Note that in this picture, I've used a total of three redstone repeaters. The first tone, the one on the right, has a repeater pointed at it so that the redstone wires don't cross, but if you make it a different way, you don't need that one.
The important thing is to make sure that the second tone (in this case, the one on the left) is four delay clicks after the first one. That is, one fully-delayed repeater.
I've found that that makes the best doorbell-like sound.
We rarely think about what musical notes a typical doorbell represents, but the ding-dong sound is usually either an E followed by a C, or an F followed by an A. For this demo, I used a C and E, but here's a handy chart from the Minecraft Wiki about using musical note blocks:
So for the first block, you'll want to right-click it 10 times, and then for the second, you'll want to right-click it 6 times.
That's how to get that distinctive, doorbell sound! Here's a video of it in action: