There are several ways to discover recipes for alchemy.
1) Experiment! When you access the alchemy table, you have two options - Create, and Experiment. Experiment allows you to discover new recipes by combining multiple ingredients together. Higher levels of your alchemy skill allow you to place more ingredients in the experiment process, allowing you to discover more potent recipes. Once you've discovered a recipe through experimentation, it is permanently acquired and listed in your Create menu for ease of use.
2) Purchase/find recipes. You can find recipes in various locations, and purchase them from several vendors as well. One example of such is...
...in Star Camp, not too far from the start of the game, you can access the Fence that has numerous alchemical recipes for sale. Not sure if this indicates the relative scarcity / secrecy of potion recipes in general, but it's a good place to start.