How do you hook up or connect a hardware
compressor? Compressors are used in SERIES with the signal you want to compress. Other signal processors that need to be connected in series are Limiters and Equalizers.
Option 1: If you're using a stand-alone preamp, you would connect the compressor after the preamp. So it will be:
PREAMP OUT ----> COMPRESSOR IN
Then COMPRESSOR OUT ----> rest of your signal chain (maybe to a mixer or audio interface).
PROS: If your preamp is balanced, and your compressor also has balanced inputs and outputs, then your whole signal chain will be balanced.
CONS: You'll need lots of cables. Especially if we're talking about a left and right channel setup or stereo mix compressor.
Option 2:You can also use a hardware compressor with your mixer. If your mixer have INSERT jacks at the back, you can hook up your compressor via these jacks. This will save you some cabling and make your setup more neater. Cons : You'll have unbalanced connections from the INSERT jacks to the compressor, and from the compressor back to the mixer.
Is this a problem? Maybe not. We're just talking about a short run of a few feet here in a "controlled environment." So running unbalanced may not be an issue.
Below is a picture of the back of the mixer showing the CHANNEL INSERT where you can hookup a hardware compressor, EQ, limiter.

But you'd need a special type of cable. Basically, you'd need an
INSERT CABLE, something like this.

At first glance, the black plug (on the photo above) looks like a stereo jack. Nooooo... it's not a stereo jack. It's called a TRS jack. (TRS stands for TIP-RING-SLEEVE).
An INSERT cable is a special type of cable. Basically, the black TRS plug (from the photo above) is wired like this:

This single jack is carrying both the send signal (that will go to the compressor) and the return signal (from the compressor).
I repeat... it's not a stereo jack. It's not carrying 2 channels. There is no left or right channel here. This is carrying only a single channel.
At the other end of this TRS jack, you'd notice there are (2) TS (TIP-SLEEVE) jacks. The White TS jack is labeled TIP. The RED TS jack is labeled RING.
The TIP TS jack (WHITE jack) goes to the input jacks of your compressor.
The RING TS jack (RED jack) goes to the output jacks of your compressor.
HINT: RED jack (think of the letter "R") is the RING jack... which is the RETURN path from the compressor
Make sure you don't swap the RIP and RING jacks when connecting to your compressor. Otherwise, you won't get any signal.