I think it's important to take both of the posts above this one seriously and not dismiss them as "not in my experience."
If you want leverage in any negotiating situation, you need to be able to walk away from the negotiation if the final terms are undesirable. The party with the best "next-best option" is usually the one most willing to stand their ground on terms, or walk.
That means you need to be prepared to lose your job when you discuss changing its terms, which implies BOTH that you should have other offers AND that you should know your boss might fire you on the spot (or worse, talk you into rejecting the other offers and also quietly stop considering you for advancement in your current role).
There's something to be said for communication style. You can do essentially what top-GP suggests, but without the high-conflict ultimatum -- basically, communicate your worry about your salary in a series of low-drama conversations, in which you can calmly suggest that your research implies that you'd be able to make $X in a similar job elsewhere, but really enjoy your current job, etc.
The key, of course, is always to understand your BATNA: Are you actually willing to leave? You can play a significantly more daring game if you're prepared to lose, rather than accept status quo or a modest improvement.
Please note that I do encourage doing "research" - it doesn't have to go all the way to an offer, but what I mean is to build confidence that you can indeed get one at the given salary. This is your BATNA, but because you're not giving an ultimatum, you don't have to walk away to a new job immediately - you can just start looking.
I would never tell my employer that I had another offer and was going to accept unless they met my demands. I'd keep it in my back pocket and then if they didn't respond to my treating them like an adult then I'd just inform them I was quitting and then I would. People who operate that way aren't worth working for!
If you want leverage in any negotiating situation, you need to be able to walk away from the negotiation if the final terms are undesirable. The party with the best "next-best option" is usually the one most willing to stand their ground on terms, or walk.
That means you need to be prepared to lose your job when you discuss changing its terms, which implies BOTH that you should have other offers AND that you should know your boss might fire you on the spot (or worse, talk you into rejecting the other offers and also quietly stop considering you for advancement in your current role).