I suggest you read about Change Management to get a good idea. It can be a slow process but it doesn't have to be. The basic requirement is not time but rather achieving a number of necessary steps. If the people buy in and you and your team deliver on the small wins, it can be done quite quickly. When you search, look for the "eight step change process". It's not the only reference and I don't recall the author at the moment, but it makes the key steps very clear.
Key is to establish a sense of urgency, one that everyone in the organization feels. You need to get buy-in from your management team or alternatively, your effective change agents. As with any change, you (or you and your team) need to develop a new vision and you need to preach that vision relentlessly and most of all, get buy in from everyone to the vision. You need to form objectives and develop tactical plans to reach that vision and those objectives, actions that are assigned as "I commit to this, to be done by this day, with this completion criteria". Through these action items, you guide your team toward making small, confirmable and quantifiable wins. These wins, tied as they are to your objectives, will naturally build upon one another and will combine into larger wins.
If you achieve buy-in quickly and have a get-it-done team, you can make large changes quite fast. Getting buy-in to the vision, objectives and necessary action plan usually takes the most time. And remember, you're looking for small wins first, not grandiose wins. Achieving and celebrating the small wins build confidence within the team, energizes them, and leads to the big wins and the change you want to achieve.
But don't only follow my quick comments here. Look up the change management process. I think the 8 step process I am thinking about while writing this was John Kotter's but there are many other references on this topic.