The glued up block of wood looks enormous, so there's a great feeling of less-work-than-you-thought once the snail is cut out.
I use my bandsaw. But what if you don't have one? An efficient, traditional, pre-electric method involves working the wood grain: You saw off what waste you can then create a series of cross grain cuts down to your line. Chop off the short-grain waste and clean up with chisels or gouges to the line. You can see me do it in the intoductory lesson to the Pelican project, here about 5 minutes in. I've used this method many times and it's surprisingly fast. You'll see me at it again in the next lesson too.
We don't need the sort of accuracy here that we wanted in the Pelican carving. If, however, you wanted to be really accurate: either place a reversed drawing exactly lined up on the back side of the wood, giving you 2 registering lines between which to work; or use a carpenter's square to check the squareness of your cuts and finished faces.
After cutting out we come to one of the most important parts of this project. Thinking before we start! And the most useful thing we can do to help our mind's eye? Make a little model. To scale if possible.