seycyrus said:
You mean for your postdoc?
Great idea! See if you can find their phone numbers and give them a call. No need to be shy. If the lab is within a few hours, I'd seriously think about showing up at a colloquia or something.
Dr. So and So,
I currently attend the physics graduate school at kick-*** U and will be finishing my PhD this summer. My disertation title is such and such. I came across a few papers that your group has published, specifically, this-one and that-one, and they were extremely interesting.
Are there any openings for postdocs in your laboratory? If so, could I send you my CV? I'm actually going to be in your area, on the 5th of next month. Do you have any time available to meet?
Dr. Me
I prefer just going with "I have included a copy of my resume for your reference" in networking emails. It saves the step of them having to email you back just to say "resume please."
I also prefer not to straight out ask for a job but to ask for an "informational interview," without calling it that, to learn more about opportunities in the field. If there's an opening and you're qualified, they'll usually just recommend you apply formally after you hit it off while talking. Even if they don't ask you to apply, you sound less desperate and more informed if you ask about a job after hearing more about the opportunity and getting to know the person a bit first. If at all possible, I wouldn't even bring up that I am looking for a job until I could casually work it in during an actual conversation. Meeting in person is also always preferable. And be prepared with questions and follow-ups.
I like to start if off with a "Dear ...," or "Dear ...:" depending on the status difference, although being a little more personal is sometimes required. The level of formality may also need to change considerably after the initial email.
For more competitive jobs you'll want to start this early and keep up with people - maybe attending conferences or asking about your or their research or just keeping them updated on your progress every once in a while. Not everyone will be open to this of course, but the friendlier you can get the better as long as you are not overwhelming. It's very easy to be overbearing and people will be easily put off if they see through what you are doing. It has to be genuine.
You are marketing and selling yourself, and there's a lot more to effective marketing and sales than simple unsolicited email

.
Of course, sometimes none of this is necessary and you can get in through an online application. Networking is also much less effective if there is a formal committee reviewing the applicants. Then again, I still haven't heard back about the online application I submitted for the job I have now. Getting to the committee turned out to be the hard part.
To get back to your original question, I'd go with formal and very brief emails asking whomever if they would be willing to speak with you about their research. Include a line about your research and something about your interest in theirs. Attach your CV "for reference." Include your contact information.
Also, don't expect everyone to respond. The most well written letter may only get you a 10% response rate. If you plan for that you can roll with it and be effective. Just don't be surprised if getting a job is tough work

.
If someone with more experience in academia wants to correct me, please do. The above advice is more business world oriented. In this case, I can't see how the two would be any different though. (N.B. opinions also vary in the business world.)
Your career services office should be able to help you too. They advise on this stuff for a living. You can also probably arrange a mock interview or have them look over your letter before you send it. Just take their opinion as one of many, and make your own ultimate decisions.