In Fortune magazine's February 2008 issue there is a "100 Best Companies To Work For" article. There is also a nice article titled "How to Get Hired by a 'Best' Company". This article reminds me of many I have read over the years regarding tips on how to better your chances of getting hired or even improving your resume. Although I generally find these articles helpful, they can be overwhelming to the person who has not gone through the process of leaving their employer and searching out a new employer. For those people I suggest breaking down the process into segments.
First, have you decided to leave your current employer or can you salvage your situation? A good blog on this topic can be found at Resigning.
Once you have decided to move on you should update your resume and have someone (career manager/mentor) who will give you honest feedback look it over and offer criticism. Ideally, partner with a recruiter to assist you with this.
Next, identify the top 20 companies you would like to work for and then ask your network if they know any hiring managers at those companies. Direct contact with a hiring manager is important to increase your odds of a face to face interview.
Now the real work begins. Start applying through your contacts and the old fashion way if you don't have contacts at your targeted companies. Many of the people I know apply through a company's website and then wait. I often hear that they applied months ago and never heard back. This does not surprise me. There are many reasons why this process is delayed and inefficient but that is another blog for another day. Take the time to go into the company (if it is local) and drop off a printed copy of your resume and cover letter in a nice binder. Be sure to ask who the human resources manager is so you can follow up later with a direct phone call. Also, inquire if there are any interviewing sessions scheduled in the upcoming weeks.
After you have applied to all the companies on your list, set a schedule to follow up with each one. I recommend calling or emailing your contacts every three days until you have set an interview or learned that the company is not hiring. As you manage your follow up communication continue to look for additional companies to apply to. Don't assume you will find a new job among the initial companies you listed. Try adding two new companies each week. Remember, if you feel like you are not making progress don't despair - ask your career manager/mentor to troubleshoot with you.