This is tough question. On one part you need to make sure you are getting paid a fair amount for your work. On the other, you have to make sure that the client is paying a fair price. The dilema is that most peoples quote equates to them getting grossly underpaid or not getting paid at all.
What is the client's budget. Important to know that very few will want to disclose their budget because they want to hire you for the least amount possible. Try using a project discovery worksheet and hand it to them to fill out. It should ask questions about their desired outcome, timeframe, and of course, budget (important to assure them that this is not for quoting purposes, but to better "explore" possibilities). A $1 pixel image on budget is not the same as a $1500 Photoshop'd high quality image.
Clients seem to be more forthright when they understand you want whats best for the project within their budget.
Spend lots of time on your proposal. If you get it wrong, it is going to hurt (your pocket, your portfolio, future contacts) Remember, clients memories are not writen in stone. always create a proposal and always put in the time to make sure it covers everything (So nobody can say - I told you...) Make sure it covers both client and contractor responsibilities, expectations, requirements, payment terms, terms for changes outside the proposal, and everything else you can think of. Since clients often have a larger scope in mind than they communicate, a couple hours on this document could save you dozens later.
Always, charge by the hour. A base fee (your hourly rate x expected hours x OOPS TIME (10 to 20%), plus add any additional hours over base fee at 80% - 90% of your hourly rate. A project is never finished - ever. Don't let the client abuse you with unallocated time.
Always up your estimated cost by 10%-20%. You will loose work over this, but especially if you are new, it will save you in the long run. So do yourself a favor and give yourself enough time (because asking a client for more time/money is generally not a good habit).
Most Important - Collect fees up front. Or at least 50% up front and X% at a predetermined milestone(s).
Make sure that the 50% covers your costs up to milestone 1, because so many clients abandon projects. (Don't Pay)