Being a consultant, the opportunities I get to do project management are quite few. Still I believe many of our customers can benefit from the advantages of doing some sort of agile method. Come riding in on a white horse yelling "You are old fashioned in-effective conservatives wasting loads of effort on your specs and docs! You will go over budget if you do not join the society of Agile developers!" won't necessarily convince management that this is the way to go.
So I take some small steps to build a small proof-of-concept, merely by applying it to my own daily routine. Most developers who like to organize their own personal work in some fashion, be it writing stuff down in a notebook or filing issues in an issue tracker, will recognize these steps as mere common sense.
It can be handy to note that these routines could also be absorbed into the project on a higher level, and that is essentially when your project becomes agile.
Step 1: Ask people what they are doing and tell them what you are doing
Each morning I take a round around the office and ask "So what are you doing today?". Most people answer "Same thing I was doing yesterday, of course. Otherwise I'm going to this and that meeting". This answer points to to some of the key issues agile methods try to address (task breakdown to easier track progress).
I'll answer back "Right. Just to let you know, yesterday I completed task X. Today I'm gonna do task Y.".
Step 2: Transparent progress
I track all my tasks on the wiki. Each time I discover some new task I think needs doing, I add another item to the task-list and grade it with a complexity rating from 1 to 5 (jelly beans, story points, etc). Each week I grab a handful of tasks from the list matching the sum of jelly beans I did the week before. If one task starts taking up more than one day, there probably is some problem or obstacle I want to address to the project manager.
Step 3: Expose your problems
The number one reason for projects going wrong is task-completion being held up by dependencies, or impedements. I can not do task X before task Y is completed. To relieve waiting-time as much as possible, I maintain a list of impedements my project manager is aware of, and as long as respective impedements have not been removed, I move my progress onwards with on another task that does not have the same dependency. If you are going to blame the lack of progress on something or someone, do it as soon as possible.
Step 4: Demand short- but concrete requirements, sorted by priority
The elements in the mentioned task-list have a couple of common traits. (1) They can be completed in less than a day, and (2) they are either completed or not, i.e. they are formulated in a concrete way that leaves no half-way completion. I've either done it or I have not.
The task-list is also prioritized. I initially just pop in new tasks at the bottom of the list, but the project manager is free to move things upwards to the top of the list as he sees fit. The only thing I demand in return is that I get to complete my current task before moving on to a new one.
In the end..
People will start to pick up on my routine. Management will notice the progress, and co-workers will copy parts of the routine when they see it is working. Hopefully the concept of jelly beans or story points will quickly be shared by the team, so we can start working together on improving our weekly jelly bean consumption.
It may be that other developers are doing leaps of progress way beyond my tiny tasks, but I will claim that we are more effective when we have smaller tasks to focus at one at a time. It forces focus into your development, and you spend less time switching back and forth between various tasks, meetings and lunch.
The biggest "issue" with agile methods is that is exposes the developers' progress to the project and embraces total honesty. Traditionally, developers sometimes end up in an evil circle of reporting progress while still not having completed previous tasks, thereby pushing more and more work into "last night shifts" that can have devestating effects on both the project and the developer's personal life.
Sucumbing to total honesty can be uncomfortable for developers, as they will have to admit lack of progress and their problems, but at the same time it will get easier for the team as a whole to discover and address these problems. In the long term this will lead to a better relationship between team-members and management, and increase efficiency as all problems are dealt with as early as possible.
One final note; I call it sneaking but still your intentions should be clear to everyone. If they ask where you your ideas, say it clear: "It's a really interesting method called XP/Lean/Scrum/etc".
Got a bit side-tracked here in the end, but hopefully this is enough to get you started. Happy sneaking!