Unlike traditional machine learning methods, humans often learn from natural language instruction. As users become increasingly accustomed to interacting with mobile devices using speech, their interest in instructing these devices in natural language is likely to grow. We introduce our Learning by Instruction Agent (LIA), an intelligent personal agent that users can teach to perform new action sequences to achieve new commands, using solely natural language interaction. LIA uses a CCG semantic parser to ground the semantics of each command in terms of primitive executable procedures defining sensors and effectors of the agent. Given a natural language command that LIA does not understand, it prompts the user to explain how to achieve the command through a sequence of steps, also specified in natural language. A novel lexicon induction algorithm enables LIA to generalize across taught commands, e.g., having been taught how to "forward an email to Alice," LIA can correctly interpret the command "forward this email to Bob." A user study involving email tasks demonstrates that users voluntarily teach LIA new commands, and that these taught commands significantly reduce task completion time. These results demonstrate the potential of natural language instruction as a significant, under-explored paradigm for machine learning.