This will vary for each freelancer, but for me…
The first thing I look at is whether they are a friend, or someone who might bring me consistent work in the future. If so, I usually give them the friend discount (anywhere from 10-50% off, depending). If it is just a one-time deal with someone you don’t know, charge them the full rate.
Every designer’s rate will differ, but given your talent and experience, I would charge between $50 - $75 per hour. I don’t usually do flat rates unless it’s something I’ve done enough in the past to confidently know I can do it within budget.
Once you have a good idea of exactly what they want from you, quote them an estimate. Say something like:
"My rate for this kind of design work is $50/hour, and I expect to need 6 hours to complete your design. So I’m going to estimate a full cost of $300."
Then get half up front as a down payment, so you know the client is serious and isn’t going to flake on you. (When sending them proofs for revision, watermark them, or send low res files. Until the remaining balance is paid in full, hold the hi-res file hostage.)
Also, make sure your responsibilities are in writing in the email. Are they expecting you to provide a physical print of the design? What kind of digital file do they need from you?
And make sure you have a sentence in your quote about revisions. You don’t want them to ask for weeks worth of revisions, and you’ve only quoted them a cost of six hours. So something like:
"This estimate includes two revisions, any additional revisions will be charged at the regular hourly rate."
You can put this all in a contract if it makes you feel safer, but I’ve found email agreements are just as good, and haven’t had to take anyone to collections.
Beginning freelance designers don’t always have the confidence to charge these kinds of rates, but your work is worth it. If they want what you do, they should pay for it. Giving discounts is fine for causes and charities and projects you believe in, just be careful, anyone who has received a discount in the past, will expect it in the future, and you will find your work undervalued very quickly.