Both baker's and brewer's yeast are products of a one-celled fungus called Saccharomyces cerevisiae. In food, both yeasts turn sugar and starch into carbon dioxide bubbles and alcohol. While baker's yeast is primarily used to bake bread, and brewer's yeast is primarily used to make beer, you can substitute one for the other. However, if you're baking with brewer's yeast, you need to make sure you're using the active version.
In dough, baker's yeast feeds on the starch from your flour to make the carbon dioxide bubbles that cause your bread to rise. It's available as a dry powder or in compressed cakes. In addition to bread, baker's yeast is used to leaven sweet goodies such as coffee cake, croissants and brioche.
Brewer's yeast, also referred to as beer yeast, turns liquid into alcohol. There are a number of types of brewer's yeast, each geared toward creating a different type of beer. You can find brewer's yeast in liquid or powdered form.
Whether you're making beer or bread, you can substitute either yeast for the other in equivalent amounts. However, brewer's yeast has a bitter flavor, which might not make a good choice if you're making a leavened sweet, but may create a tasty and savory bread. Additionally, baker's yeast is not as flavorful as brewer's yeast, and may not create a distinctly beer taste in your home brew.
Tips
You want to test, or proof, your yeast to make sure it's alive before you get started making your bread. To do this, mix your yeast in warm water, ideally from 90 degrees Fahrenheit to 100 degrees Fahrenheit, with either sugar or flour depending on your recipe, and set aside for 5 minutes to 10 minutes until it is foamy and bubbly. The foamy liquid is then added to your flour and the kneading process begins.