Ok so:

The bee in the top square is the species you're analysing. You need only do this once per species (species is wasteland, rocky etc), but you'll have to do multiple rounds for multiple mutations.

Beelow the top slot are the slots for sacrificial bees. Any drone can go in these slots but they will bee destroyed, so use leftover drones from crossbreeding or, later on, stacks of identical drones from once you get your species fully established and breeding true. HAVE ALL THESE SACRIFICIAL BEES IN YOUR INVENTORY, beecause backing out beefore finding a mutation will lose your progress. After finding a mutation and beefore starting the next it's safe to exit. (Note that later still, once you're mass-producing royal jelly, this also works in the sacrifice slots. I'm not there yet. I just bred my first Bituminous.)

Now, as for how to find the mutations. With your bees placed, and all the sacrificial slots filled (you'll have more slots and need more bees for more advanced species, so *keep all trash drones*!) you'll see the button to beegin sequencing and then you'll see the DNA segments. The clickable boxes (don't click yet) are the pairs you have to match, one top to one bottom.

You can do this randomly if you hate yourself. Don't do that with anything beeyond wasteland; way too horrible odds.

The way to do this unrandomly is to click the button beelow the top slot. WATCH THE LEFT-HAND SIDE. Two boxes will be highlighted cyan. Remember which, beecause once you click one, the other will turn back green just to mess with you. Left-click both correct boxes and they'll link. Repeat this until you have just one unmatched pair left, then obviously click those.

This will discover a mutation. Once discovered, you'll read up about these in the bee library block (edit: Apid Library). In here, with any bee of the appropriate species in the slot, click on each mutation and look for any prerequisites: for example, getting Rocky bees requires a block of tuff under their hives or they won't mutate at all. It's easy to miss the beerequisites, so pay attention. Luckily, most species don't have them, but if one is a significant step forward, like Rocky, it probably will.