For example, I would like the user to be able to set their home location as a 6 digit number. Then they can just ask my skill for an update, "when's the next bus coming", rather than having to say, "when's the next bus coming to location 123456".
You can persist information using either a database or by passing information along in the session object. There are lots of examples and information about using DynamoDB, such as this Alexa cookbook example.
The session object allows passing data along from each intent to the next, but only persists for the life of the session. The Amazon documentation contains the information about session, but the specifics will depend on the language you are using (eg. Java or NodeJS)