Compressors usually come before any boosts, overdrives, fuzzes, or distortions in order to minimize the noise floor of the signal chain. Compressors will take the whole signal's lower dynamic floor, including the white noise, and amplify it, so placing it as early as possible in the chain keeps that extra noise at a minimum.
There are valid arguments to support both ways. Ultimately it depends on the compressor you are using, the dirt you are using, and the way you are using them. I use a Diamond- with a high cut filter which helps cut down on noise- and I typically like it after my OD.
If you have a wah pedal, you may want to try placing the compressor after the wah. I recommend trying the compressor in front of the wah and after to see what works best for you. Obviously, try using both together when experimenting. But, if you'll never use them together, the order is not critical.
Personally, I like placing my compressor early in the chain...before dirt. But, I rarely use compressor with dirt, so order is not that critical. Dirt pedals tend to have some amount of compression already, so I find using a compressor with dirt to be a bit redundant. For example, a TS circuit is highly compressed.
If I do want extra compression with dirt, I use my Damage Control Liquid Blues OD stacked with other dirt pedals because it has a built in Optical Compressor that does not add much noise.
As long as a compressor has Attack, Sustain and Volume controls, it's pretty easy to reduce the noise it creates by how you set those knobs. In general, setting the Sustain lower than the Attack and the Volume at unity will help to reduce compressor noise.
The Keeley Red dirt has noise, just turn the gain up and its there. The EP boosts this noise, and a compressor raises the noise level too. Its what guitarists have been dealing with for over forty years. Noise reduction pedals were invented because of this.
i do mine before my dirt. it adds noise but i have a volume pedal just before my delay. when i'm not playing my volume pedal kills any sound going to the amp so i don't have to worry about the added noise from the comp.