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So you would like to make your own bitpop or chip music? OK. I'll share what I know.
First of all, all art, such as music, differs greatly in taste and style from person to person.
I will make this a strictly technical guide. And I will be talking mostly about the Nintendo Entertainment System (Famicom in japan) as I base most of my music on this sound chip.

A basic element of "true" chip music is simple waveforms, such as Pulse, Sine, Triangle and Noise.
If you want to make music based on a specific chip, you'd better know the limitations of that chip, and what waveforms are supported by it, or you won't get a genuine sound.
To achieve the limitations without having to do a bunch of tedious work, it might be good to use a tracker or other software specifically designed to emulate the chip you want to sound like.
The most prominent example I can think of for that is Famitracker, that has the exact same sound types and channels supported by a Famicom/NES sound chip. So if you want to make chip music and be sure to succeed, use Famitracker. Even if what you produce won't sound good, it will be playable on an actual NES.
As Famitracker has excellent documentation and very well written tutorials (found through a search engine near you) I won't be going into detail on how the program works. Just remember that you have to create a new instrument before you will get any sound.
If you do not wish to use specific software, these are the "restrictions" you should keep in mind if you still want to create a NES-like sound:

The NES has five mono-channels. Two of them feature pulse wave channels with a variable duty cycle of 12.5, 25, 50 and 75%. The volume for these channels can be set to 16 different levels. Hardware pitch bending is possible and the frequencies used range from 54Hz to 28 kHz.
There is a fixed volume (on or off) triangle wave channel with pitch bending. Frequencies on that channel range 27 Hz to 56 kHz.
There is also a white noise channel with 16 volume levels and 16 pre-set noise frequencies. I don't know the exact frequencies. Additionally there is a differential pulse-code modulation-channel capable of playing any sound.
If you want to play samples that sound like those on the NES though, get a program that can convert your wave-files to 1-bit, as this is most true to what imported samples actually sounds like on a NES.
 
Now you might understand why it is easier to use software dedicated to the task rather than trying to simulate the sound.

Now onto some different waveforms.

Triangle

This is an image of a triangle waveform, commonly used when composing chip music
At low frequencies this waveform is commonly used as bass in NES compositions. At high frequencies it produces a "flute-like" sound. It can also be used as tom-tom drums by sliding from high to low frequencies. Keep in mind that this channel has a fixed volume on a NES, meaning it is either on or off.

Pulse

This is an image of a pulse waveform, commonly used when composing chip music
This is a very interesting waveform as it is possible to vary the duty cycle of the sound wave in order to produce different sounds. The closer to 50% (half the time on, half the time off) you go, the more hollow it will sound. If you set a very high or very low duty cycle you will get more of a creaking sound. This waveform is mostly used for the melodious part of the song as the two channels on the NES can be used to create neat chorus, but it is also in my opinon well suited as bass, depending on what sound environment you want to achieve.

Sine

This is an image of a sine waveform, commonly used when composing chip music
Is the waveform that most resembles that of an acoustic guitar. The sound is even and soft. It is best used at higher frequencies where it sounds a bit like whistling. At low frequencies it can be hard to hear the difference between notes.
This waveform does not exist natively on a NES unless manually shaped on the DCPM-channel.

Sawtooth

This is an image of a sawtooth waveform, commonly used when composing chip music
Sounds very "sharp" and can be used both for melodies and bass. Its clear, crisp sound makes it especially suitable for arpeggios. This waveform can not be used natively on the NES, but a lot of Amiga music composers use this wave form frequently.

Noise

This is an image of a noise waveform, commonly used when composing chip music
This "waveform" is commonly used for drums, as, if shaped correctly, noise can sound quite similar to drums. High frequencies are best suited for hi-hat/ride, mid frequencies for snare, and low frequencies for bass drum or kick.
It can be difficult before you learn how to shape the noise correctly. I would suggest using a quick linear fadeout as the base and then tweak it until you're happy with how it sounds.

As a last tip: A lot of the beauty of chip music lies in making rich compositions from seemingly scarce resources. Try to get the most out of every channell!