So I have an upcoming performance review / salary increase and I am at a point in which I believe I will need to negotiate a larger raise than what is to be proposed.

As I suspect this may be the case I have been reading as much information on the subject (negotiation) as possible. I work for a great company and fortunately I work under some really talented and reasonable managers.

Unfortunately, I am not sure how best to bring up the subject. I don't want to sound greedy and I don't want to start off on the wrong foot. For the sake of argument, assume that I am actually worth more than I am being paid at the moment and I would like to make a counter offer for a relatively large increase (say, boss says 4%, I would like to counter with 15%. I know that seems very large, but I believe I have a case for it.)

My question to you, those who are/have been on the other side of this scenario, is how should I start the conversation? What approach would make you most receptive to my plea?

I've never negotiated before and I just don't want to start off on the wrong foot. My direct manager is a very straightforward individual, so sugarcoating is not necessary here, but at the same time, I don't want to seem overly aggressive or demanding.

Thanks in advance for any advice you can offer.