I recently asked for a raise, I did an online course from @dmitryopines on that twitter. Cost 17 quid but it was really useful.
Basically try to work out why you staying is good for the person who makes the decision - e.g. are they trying to keep everything stable? Or do they care about numbers? Or do they value innovation? Whatever you think it is tailor your approach to that.
Then think of your number - don't base it on what you earn. Look at the market, then add more for your expertise in the job. You know people at the company, you are proven. They don't need to find somebody else etc etc. Then add a bit of leeway so you can negotiate.
Anticipate their objections - either can't or won't. Think of things to say back. Plan the conversation. Ask them when they can give you what you are asking for if they can't do it now.
Think of other things you ask for that aren't just money. E.g. improved working conditions, extra holiday, or even just finding out what they think of you.
There is more stuff but that was the basics.
I did all of that, went into the meeting, gave my speech and the guy basically said "oh, I thought you were going to ask for more, no problem". But I was PREPARED.
E-Learning: Negotiating Your Salary — ExplainTrade that's the link if you're interested. I was cos I am so bad at it.