Classically they would tend to melt the housing of the chips off with some fairly unpleasant acids to reveal the chip and bond wires. Today there are some slightly nicer chemical means (though trickier) and some do it with abrasive methods*. If you happen to be able to find raw dies or it is one of those old school ones with a simple covering then fantastic.
*most of the ones I ever see in labs will be using metallography style sample prep machines (pregrinding machine for metallographic sample if you want a choice search term for a shopping search), which is not a terribly cheap hobby. However a surface plate and fine ruby sanding/lapping/grinding paper or something similar might get it done.
Microscopes (optical in some cases, scanning electron microscope aka SEM in others).
From there you grind down layer by layer (some chips are single layer, others not so much, sometimes there are also security measures but that is usually a thing for those also doing electrical analysis) making a complete image as they go (stitching it a lot and possibly sorting things if your grinding reveals multiple layers at once)
There was a nice talk on it at C3 a few years back (think between 24c3 and 27c3) but I could not find it last night when making that reply. It covered how it became possible to do it outside high end electronics research labs (be it university or big chip maker) and a few searches on it say it has got a bit better still.
So yeah unpleasant chemicals, tooling investment, microscopy, time to stitch things together (though software can help) and it almost always necessarily being a destructive process for what might well be rare, expensive and hard to come by samples*, possibly multiple at that.
*it is one thing to put your fun stuff money into buying say a neo geo and attaching scope probes to it, maybe soldering a few wires and then doing a bunch of tests, either to keep or sell on when done for as much or maybe more than you paid for it, quite another to basically destroy it.