You have the most power to negotiate a salary after you've impressed your future employer in interviews, but before you sign an official job offer.
Most employees will informally offer you the job before they give you anything to sign, and this is a good time to talk about what you want.
Your new employer wants to hire you, received buy-in from other team members, and has no desire to keep interviewing. More than anything, they're anxious for you to start work. This is the time; ask for more money.
To determine how much you should ask for, trust that the employer has given you a healthy and fair salary to start with. But don't undervalue yourself and know that all employers expect you to do some negotiation. Indeed, many employers see candidates that negotiate as high-performers. Figure out the salary you want, and then ask for a bit more to allow room for compromise.
Practice how you'll lead the conversation, and try something like:
"I'm really excited to work here, and I know that I will bring a lot of value. I appreciate the offer at $58,000, but was really expecting to be in the $65,000 range based on my experience, drive, and performance. Can we look at a salary of $65,000 for this position?"
Employers may balk to start. It's in their interest not to pay you more of course, and get you to work at the lowest possible salary. So, expect initial rejections, like:
"So glad to hear you're looking forward to working with us. We're really looking forward to having you. The salary we offered is what we have budgeted for the position and we feel it's a fair compensation."
This may sound like it's the end of the conversation, but it's not—don't back down! The key here is to continue to show your enthusiasm and stay confident in your abilities. Try:
"I understand where you're coming from, and just want to reiterate my enthusiasm for the position and working with you and the team. I think my skills are perfectly suited for this position, and are worth $65,000."
Now, don't say anything else. Let the silence lie. Don't try to fill it with more words or justifications. Just wait for the employer to reply. When she does, it may sound something like:
"You'll really be stretching us, but I'll see what I can do."
This isn't the time to feel bad or uncomfortable. Simply reply, "Great, I appreciate that."
The employer will likely come back to you, and accept your offer or offer something in the middle ("We talked it over, and feel you're going to exceed our expectations and be a great addition to the team. I'm happy to offer you a salary of $62,500"). If you asked for more than you wanted, you should feel success in accepting either outcome.
The biggest factor in determining whether or not you get a higher salary is based solely on whether you ask. So ask. The vast majority of companies are willing to negotiate salary, but the vast majority of employees never even try.
Research a fair salary, act professionally and with respect, and remember that while you may feel nervous, this will actually be the easiest money you've ever made. Go for it!