Most companies like the idea about looking within first for job openings, unless of course if the decision to look outside first is motivated by political reasonings (Eg. VP's poker buddy, complete lack of faith in the talent of internal resources, finding yes-men for political power plays, etc...)
The reasoning for looking within is that it is one of the few real tools a company has to battle attrition for a number of reasons like people leaving the company for better career development. If they know that you are unhappy in your current position or want to grow in career and responsibility, then there may be no room to do this where they are currently at.
Of course it is good for employees too because it means that their resume is not further tarnished by a less than 2 year job hop if they are miserable in their current role. I have transferred before for such a reason where I was working in a company that had many very different business units, but the business unit I was in was so festeringly political, hostile to employees, and sufferring from careless self immolation to the point of hemhoraging money at a spectacular rate. I started to accept that nearly all IT jobs were this horrible and painful to work for in real life, so I wanted to make a committment to suffer at just one company for more than 2 years. When a transfer came up to a new division that fit my skill set, it seemed like the perfect opprortunity to retain tenure and escape a situation that had me thoroughly depressed. The process was great (however the new division turned out to be the single worst place I have ever worked for, bar none, considerably more terrible than the division I left, but that is beside the point).
Knowing that many companies look on this favorably, the most important things to keep in mind is that you want a transfer to be smooth so that the old manager, and the new manager don't both end up holding a grudge against you, or each other.
In interviewing for an internal position with a new manager, make it clear to him that you hold your current responsibilities in high regard and as such you wish to have at least 4 weeks notice to make sure you aren't leaving a mess behind.
Be honest to both managers about your career goals and your loyalty to the company as a whole.
Keep an eye out on the job postings for that perfect position in the other department to open up. Most companies have a seperate job board for internal people where jobs are posted for a period of time before they go public on the website.
Don't bring up a desire to transfer to a new division to your current manager in conversation. This will just make him think that you are unhappy and there is not much that he/she can do about it.
Most companies have an annual review process, and part of this involves the manager finding out what your long term career prospects are and how the company can help you meet these. This is the perfect opportunity to bring up a desire for career advancement. I would still avoid talking about transfers at this point, but the manager will know if your career prospects don't align with his current business unit at all and if another division is more suited for you. Let the manager figure this out for himself, don't straight up tell him that you wish to transfer.
It is frowned upon in most places if you try to transfer too early. Check the employee manual for rules on internal transfers and see if your situation is acceptable. Generally an annual review means the perfect amount of time in your current role before this thought should even be entertained.
Bad blood and jealousy between departments can still happen even if you do everything right. Offer to throw in some of your free time to continue answering questions for the new guy(s) in the old department as a sign of good will and generosity. This removes some of the pain to the guys in the old department and helps bolster any bridges for you to come back someday if you need an escape route. Further it demonstrates to your new manager that you really are an exceptional person and he will be delighted that such a thoughtful and devoted person has just joined the team.