I've worked in several large companies as a consultant to help customers and partners build applications that interact with our software products. Enterprise software companies typically offer access to their services through Software Development Kits (SDKs). It has been interesting watching how the technology/language trends have evolved over time.
For beginners, I would recommend Python. It has a simple syntax but can be an extremely powerful language to use. It works well for demonstrating concepts and there are an abundance of books/tutorials available.