How do you introduce (or start following) Scrum?
The best approach would be to hire a training course for every stakeholder. It means, I consider that every manager has to know what is Agile before adopting Scrum. Then the company has to hire an Scrum Master and Product Owner (or train one Business Analyst or Project Manager or other professional who knows very well about the business of the company).
Last but not least, someone has to create Scrum teams that has no more than ten members (more or less) and if you have a new project do an Inception (ceremony to define features and user stories as well) and after the inception the Product Owner has to move several user stories to the Sprint Backlog (it would be better to have user stories into the next Sprint too) to do the first Sprint Planning and you can start your Scrum journey.
This is the basic Scrum if we agree that there are many spice to add to Scrum such as: Unit Test, Automate Test Cases, Testing Driven Development (and then Behavior Driven Development), Peer Review, Architect (one per Scrum team would be the best), UX designer (one per team), Continuous Integration (CI), refactoring (that is a powerful tool if you are working with Legacy Code), Technical Debt (if you are working with old code) and Pair Programming.
Most of these practices belong to the famous Extreme Programming (XP). However, time after time every Scrum team want to improve, i.e. refactoring is great approach when you have to deal with legacy code or when you are migrating to a new platform.
As soon as the Scrum team grow up it is a good idea to move to unit test, define what is the minimum coverage of unit test and start using any kind of software to check the quality of source code such as Sonar.
Later you would automate test cases to wrap the testing up.
In the mean time, you can add any good techniques step by step to improve the development. For instance, start using Peer Review (every developer has to check the code of other in order to do a double check of development standards). If you have to deal with Legacy Code and you have to fix bugs in every sprint it would be a good idea to do refactoring in order to fix and improve the code at the same time.
When is a good moment for Pair Programmin?
Many times you has to replace developers, sometimes they leave the company or you fire them so you can start adopting Pair Programming to transfer the knowledge to the new guys or if you have a complex project.
To conclude, after many time you are involved with Scrum you have added many extra practices and I would like to say that you are following an Scrum Plus approach.