When you ask for a raise, you'll have more success focusing on the value you bring to the table as opposed to your own needs. You probably don't want to blurt out, "Hey, I've got bills to pay and you haven't bumped my salary in three years" - even if it's true. So what do you say?
It helps to think of your request as a formula, which looks a little something like this: Intro + Value + Price + Conclusion. Here's the gist of each factor.
Intro: First, preface your request with a quick intro. Something like, "Thanks so much for agreeing to meet with me. I've been working for [Initech] for [5 years]. In that time, I've helped the company grow as I grow along with it."
Value: Then, remind them of your value. List a few of your major recent accomplishments (which is why, as corny as it sounds, it helps to keep a list of these). Quantify as much as possible. "I've helped the company reach out to two thousand new clients in just three months. I created a presentation that has now been implemented in five of our other offices. The standard rate for someone in my role with this level of experience is $70,000."
Price: After you've established your value, name your price. What exactly are you asking for? For example, "I'd like my pay to match the growth I've had with this company, so I'd like to request a salary increase of $6000 a year."
Conclusion: Finally, wrap it up. End on a high note and express your appreciation. Focus on bringing even more value. "I'm dedicated to helping this team grow even more in the future, so I appreciate your consideration."
You don't want to follow this as a script, because that sounds, well, scripted. That said, it helps to have this structure in mind when you're trying to figure out exactly how you'll make the case for a raise, based on your own accomplishments and skills.