How should I ask for a raise?

Long story short: I have been at my current job 3 months and I just got promoted to do the job that my friend used to do. She brought me into the company (she had been at this firm for 5+ years) and then left, and I guess I’m the only one they trust enough to do this job correctly. This firm is filled with incompetence. I was given the job over 2 people who have been at the firm much longer than I and this is a position with a supervisory role.

I know what she was making, and I don’t expect to make that much, but I still think I should get a significant raise. I was told by my friend to write a letter because the partners are always busy.

Thoughts? Suggestions? I’m not really good at putting a value on the work I do. Should I high-ball them and then take less? I’m confused all around.

Help.