Before thinking about introducing agile development first explore which is the best fit for your organisation / project. If for example you are looking at scrum consider whether you'd use it strictly or if a more loose form of scrum, or even another method altogether might better fit. My answer then is on scrum as your agile method.
Scrum is great for projects that require innovation, where little is known and where experimentation is needed. It isn't the best fit for doing things like maintaining existing products or handling recurrent maintenance work. Fortunately though, scrum is a loose framework and you can use it the best way you can.
For maintenance work Kanban might be better for you or you might try just a few scrum elements for managing the sprint and doing things like daily standups. I call this "scrum-but", "yes we do scrum in our company but...". That's fine, don't feel bad about it.
For introducing scrum proper in your organisation you need involvement of the product owner and stake holder. If you're a small company, that guy might be one person, the boss, and in a larger one a product manager and the department head / boss. I would suggest two routes for introducing scrum:
1) you can start using scrum in a slightly looser form for managing existing work queues immediately. But look into Kanban too.
2) start using scrum in a more strict form on some new project that will require innovation, early feedback and where much is unknown. You can suggest to the boss / product owner that scrum would be ideal for this new project.
But remember! this isn't just about code, the product owner has a crucial part and must understand and fulfill his/her role. That means for example not writing all the specs up front, rather starting with the minimum, rapidly iterating, getting feedback, learning and feeding that back in and so on. Try to work with a product manager who would be as keen to introduce scrum as you are but from the product owner side, and ideally he/she should be tough enough to fend off management requests and protect the sprint.
It'll take united effort from development and product management to introduce scrum.
On such a new project, try and get the new team moved to a separate room and use post-it notes to visualise work in the various states such as backlog, in progress etc. Don't get bogged down in electronic tools at this stage, keep things as simple as possible. Don't feel silly doing planning poker with cards when you start too, once your team is up to speed you probably won't use them just say the numbers.
In my experience it is easier to introduce scrum in a pure form first then ease up on it for more maintenance type work queues. It is harder the other way round.
My final comment is to beware thinking scrum is some development panacea, it isn't. Scrum is a useful and simple framework for product innovation but explore other methods combining as your business requires it and don't feel bad about it.