Let’s get right into it: parallel compression is when you blend a compressed version of a track with the original track. That’s literally all there is to it, don’t let anybody scare you into thinking it’s more difficult or complex than that.
It’s sometimes called ‘New York style’ compression by people who want to make it seem like they are more elite than you and have top secret references and knowledge that you simply don’t understand.
It allows you to use to extreme compression settings without completely destroying the transients (aka the peaky out-y bits) of your source audio - that’s why it’s often used on drums, you can use it to bring out the room sound of the drums and the sustain of the cymbals - without absolutely trashing those spiky transients, which help give the ‘punch’. But you can use it on any source you’d like, of course (including the mix bus…). Simple, but cool.
Wet/Dry Blend Knob
Nowadays, most plugins have a mix knob or a way to blend the dry/wet levels (dry being the uncompressed or unaffected signal, and wet being the compressed signal), so you can achieve parallel compression just by tweaking this mix knob - you’re probably already doing it.
If you’re using a hardware compressor alongside your computer, you can use an I/O insert plugin to insert the compressor/FX, then there’s usually a mix slider on the plugin. Just be sure to hit the ‘ping’ button (other DAWs will have something similar), which will compensate for the latency introduced by the round trip out of your sound card and back.
There are a couple of other ways to achieve parallels compression that gives you a lot more flexibility: by ‘multing', and using sends.
Multing
Another way to achieve the same effect is to simply copy your track, compress the crap out of it, turn it down, then bring it up to blend it with the unaffected track. This is also sometimes called ‘multing' - e.g. splitting a guitar into compressed and uncompressed by multing the same guitar recording and sending one to a compressor blending the two sounds. And you don’t need to only use compression, you can EQ it, add FX etc, then blend it in with the original track.
Some people even ‘mult’ a vocal and split it into three using EQ - low end, mids and highs, treating them all differently and blending them all back together - but those people are usually mad.
This technique is cool as you can automate and add a bunch of EQ and other effects to the ‘multed’ track.
Send It / Go Full Send / Other Word Play
You can also use a ‘send’ to send the audio to a bus, and then compress that bus - you’ve probably already done this with reverb. For example, you could make a ‘smash bus’, that you send the kick and snare to, and blend that in a tiny bit with your original kick and snare. Or just the drum room mics for a section of the song. You can even gate the input, if you want. Go wild, it’s your party.