How should I negotiate the pay rate of a job?

This is an excellent question. There are lot of websites that provide an average or overview of the salary ranges that companies usually pay. You might want to checkout websites like salary.com, glassdoor.com. That should be a good start to get this idea.
Based on that you can decide how much you should ask and negotiate your job offer. Companies usually dont deny you an offer just because you asked more money. If they like you as a candidate they will be willing to negotiate. However keep the negotiations after you get an offer call. Do not negotiate before they give an offer call. If you ask too much and the HR is not able to provide it they might say to you the max amount they can offer before they decide to move on with another candidate. Good luck.

Congratulations on finding several attractive opportunities. Below are some tips for negotiating a higher salary:

1. 
   

   Always negotiate. Even if you receive an offer that you're willing to help, I always encourage folks to negotiate. Hiring managers and recruiters often leave a little extra budget in their offer and you'll never get a higher salary unless you ask.

   
   


2. 
   

   Your negotiation should be based on facts and objective data rather than feelings. Generally, when you're negotiating a higher salary, the recruiter you're speaking with has to defend the higher salary you're asking for to the hiring manager. By sharing data to drive the negotiation, you're helping the recruiter "fight" on your behalf.

   
   


3. 
   

   A few ways you can use facts to drive the negotiation:
   (a) If you have an offer from another company, do share that you have an offer. This can be a very powerful negotiating tool.
   (b) Use tools like Glassdoor, Payscale.com to get data on what salaries are like at your company and at competing companies.
   (c) Try to speak with friends/family who work at the company you have an offer from or from competing companies. This can give you some good data to share with the recruiter.

   
   


4. 
   

   When speaking with the recruiter or the hiring manager, always convey excitement about the role and the opportunity to work at the company. Stay humble and remember that while the interview process is over, you want to continue to show excitement. Your reputation can be impacted if you don't deal with the negotiations in a professional manner.

   
   


5. 
   

   While the pay is important (we all have student loans to repay) - early in your career, it's a lot more important to optimize for learning, great teammates, and a supportive boss. You have plenty of time to earn that extra $5,000!

   
   

How I would suggest proceeding, depends on your experience level?

If you are fresh out of college and just starting out I would try to negotiate a higher salary using all the tips people have given you about such as salary.com to find out what salary median is for someone in your line of work based upon your experience to start with. However, ultimately if you have limited experience it is more important to get your foot in the door first especially if its with a great company.

Give it chance first as they might offer good raises or incentives such as bonuses to offset the lower base. Once you get your experience and work for this company for few years it will open up other opportunities for higher paying jobs if you are still unhappy with your pay at the company you are working for.