Fresh yeast is the middle ground between modern dried yeasts and ancient sourdough. You can buy it instead of growing your own, but now that dried yeasts are so prevalent at stores, fresh yeast seems like a very old-fashioned product. It's much more perishable than dried yeast and can be unpredictable to use, just like sourdough.
The first "commercial" yeasts in the 1800's came from beer brewers, but the real breakthrough was when microbiologists following the work of Louis Pasteur learned how to culture pure strains of yeast. At about the turn of the century, centrifuges were used to concentrate those cultured yeasts, and we were on our way to easily available commercial yeast.
At first the commercial yeast was a slurry, Later it became "cream yeast" which was live yeast suspended in a growth medium. Finally, compressed fresh cake yeast was developed, and became the standard for bread baking. Compressed yeast is essentially the same as cream yeast, but with most of the liquid removed. It resembles soft clay and has a distinct aroma.
Because of its perishability, fresh yeast can be a little hard to find. Grocery stores sometimes sell little cubes of fresh compressed yeast, but that's a hit-and-miss proposition. I see it more often around holidays, when presumably people might be baking bread from scratch. If you do buy it, you have to hope the yeast is still viable. It's risky.
So why should anyone bother with fresh yeast?
For one thing, the flavor. When everything else is equal, fresh yeast imparts a flavor that isn't present in breads or pizzas made with dried yeast. It's not the same as sourdough, but it has a distinct flavor of its own. You might not want to use it every time you make dough, but you might want to give it a try at least once to see if you like it.
How to Proof Fresh Yeast
Since cake yeast is so perishable, it needs to be proofed just to prove its viability, and it's not a bad idea to have a backup plan, just in case the yeast isn't alive. Fresh yeast can be proofed two different ways.
First, just like dry yeast, you can add your cake yeast to the water you'll be using in the recipe, along with some sugar. Cake yeast likes water temperatures of 95-100 degrees. It should be bubbling and foamy in about 10 minutes.
The second method for proofing fresh yeast is to add about a teaspoon of sugar to the yeast and mash it together. The yeast may simply collapse into a puddle, or you can add just enough water to loosen it up. When it's lively and bubbling, it's ready to be added to your recipe.
One note: even though much of the moisture has been removed, fresh yeast is still a wet ingredient. If you're being very precise with your recipes, keep that in mind, and hold back a bit on the water in the recipe.
Once the fresh yeast has been proofed, you can use it just like a dry yeast that was proofed. However, since the viability of fresh yeast is so variable, rising times can be unpredictable. A super-fresh, very lively yeast might rise faster than you expect, while an old and sluggish one might take a lot longer.
How to Buy, Store, and Revive Fresh Yeast
If you can't find fresh yeast at the grocery store, it's not hopeless. Many bakeries use fresh yeast, and might be willing to sell you a chunk. When I buy it, I usually buy a full pound of it, and it costs a lot less than buying individual cubes at the grocery store.
Since fresh yeast is so perishable, you need to use it or find a way to store it before it dies off. I've found that freezing is a perfectly acceptable method. I divide my 1-pound block into 16 1-ounce cubes and I wrap them, bag them, and freeze them. They aren't quite as lively coming out of the freezer as they were going in, but I haven't had any of my frozen yeast fail to proof.
Frozen yeast shouldn't be introduced immediately to warm water—let it come to room temperature gradually to avoid thermal shock. Thawed yeast tends to lose its density—it melts into a puddle rather than staying thick and clay-like—and since the yeast is groggy from the chill, it can take a bit longer to become active.
If my frozen yeast is getting old, sometimes I'll use two of my frozen portions as the equivalent of one cake of truly fresh yeast. Or I'll just let it rise longer, as needed. Because we all know that a long, slow rise isn't a bad thing.