Each NoSQL database is different, but MongoDB does not support stored procedures or triggers. It has an interactive shell which uses a Javascript API to interact with the database, as well as a range of drivers supporting other languages such as
Java and Python. I think the main focus of many NoSQL databases is on horizontal scalability via various mechanisms and data models, rather than including extra code within the database.
If you want a good overview of several different NoSQL databases, try the book
Seven Databases In Seven Weeks.