I'm trying to get this sucker out. I'm guessing the plastic-rubbery trim pops out and you can see the mounting screws on the side but I can't figure out how to pop it out. I'm afraid I'll break it if I don't know the trick.

It's a Ventura CD83. Not the greatest car stereo but not bad and I own it already.

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1986 300SDL, 362K
1984 300D, 138K

I think your best bet would be to buy something like this kit:

https://www.nationaltoolwarehouse.com/44pc-Master-Radio-Removal-Set-P132647.aspx?gclid=EAIaIQobChMIwIj8i7mT1gIVlEoNCh3ErAg5EAQYASABEgJXLPD_BwE

I have one, and by trial and error (most times) I have had no trouble removing multiple brands of head units. Best of luck.

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1992 500SEL 25K
1995 E320 40K
1995 SL600 120K
2002 JX8 Sport 43K
2005 Volvo S40 95K
2006 Isuzu NPR 304K (Frankencamper)
2007 Crown Victoria 150K
2014 Smart Electric 20K

Do you first have to pull out the plastic trim that surrounds the radio and the switches above it?

Go on YouTube and see if you can find a video showing a radio installation on the make/model of the car in question. It may show you what you want to know.