Baroques are a challenge for sure. We have our vault team trained on how to drill, but whenever it is a baroque pearl, there are only three of us who try to drill them. Drilling looks easy, but there are lots of little things that just take practice to really get the hang of.
With baroques, I'd recommend marking exactly where you want to drill and then lining it up against the bit. Once it's exact, flip it around to see where the opposing hole is going to be. It can be difficult to get a pearl lined up if it's oddly shaped, but you can do things like wrap a rubber band around the cups and then tighten them against the pearl while the pearl is lined up to the bit. That way you can see exactly where it is going to drill.
Start very slowly. You really want to just make a divot so that if it pops out (which it likely will if you press hard), you'll be able to line it back up in the exact same place.
When you get through the bead (if a beaded pearl), you'll feel a very slight give in the handle. Sort of like it "popped" through. You'll also see a blast of pearl powder come out the bit side. This is the maximum depth you'll want to go before switching sides, otherwise you might blow out the back side. You can also feel this with rounds, but if you've gone that far with a round pearl, you're almost at the damage point, so typically I'd aim for about 3/4 way through on each.
If the nucleus is hard, you'll feel it right away. It will almost feel like you've got a dull bit, and your bit will dull if you hit a hard nucleus. The number one rule is don't push. Your pearl will crack. You'll want to tap it while keeping your bit sharp and cool. You might have to sharpen it part way through the drilling. If you can't sharpen it (if you don't have a grinder), you'll go through one or two bits to get through the pearl. That's better than cracking a pearl.
There is a lot more that you'll sort of just "get" after drilling for a while, so practicing on cheap pearls is a good idea. One thing to watch out for that just about every pearl driller has done at least once ... make sure the cups match. If you've got a bunch of different sizes and accidentally use a 9 and a 10, for example, you'll destroy the pearls. The drill hole will be off center and it will wobble on a strand. I've only personally made this mistake once, and it was with a "Pelosi" strand - a style we sold about 10 years ago. I was making it from loose earring pairs 12 mm Tahitians, whites and golds. I didn't notice something was off until I was about a quarter way through the strand. That was very expensive mistake.