Our first born was a month old this weekend, so I am right there with you! After surviving on two or three hours of sleep a day for the first couple of weeks, I found myself becoming exhausted. I've heard that new moms should "sleep when baby sleeps," but that's easier said than done. I don't sleep well during the day. Besides, my daughter would sleep for twenty minutes to an hour and be up again!
A friend sent us the book "On Becoming Babywise" as a gift just a week or so ago. She had used the methods for both of her sons and they are wonderful kids. I was desperate for information on "sleep training," so I read the whole book in an hour. The book says to start as early as the second week, and our daughter was over three weeks old. We started that day (last Saturday) with the plan. It's the feed/awake time/sleep plan that a couple people here have mentioned. We're not very strict with it because it's next to impossible to keep a newborn awake when she wants to sleep, but that very night she slept soundly for 4 and a half hours. She only woke up once for her feeding and then fell back asleep. I was - and am still - amazed.
The part that helped us the most for our newborn was the chapter of the book that encourages listening to your child's cry patterns. I am not a fan of "cry it out" (which shouldn't even be attempted until 6 months, so please don't confuse this w/ CIO) and had never listened to my baby cry because I was always intent on stopping the crying. The book points out that babies cry when they're tired, and I soon realized that by constantly interfering with her crying when she wasn't hungry or wet, I was overstimulating her when all she really need was a chance to sleep. As a result, she wasn't able to fall asleep!
Thanks to this book and the strategies in it, we now have a nightly routine where after she's been fed, burped, and changed, we put her to bed. We set a limit of 10 minutes of crying time(the book recommends no more than 15 minutes). If she's still crying after 10 minutes, we pick her up and give her soothing/awake time for another half hour and then put her down again when she's drowsy. We start this at 11pm right now because she's fully awake from 8 to 11 every evening. Using this method, we have found that she has been asleep by no later than 12:30 every night and she sleeps until 5:30 or so. At 5:30, she has a feeding and diaper change and she falls back asleep. She has NEVER cried when I've put her back to bed after her 5:30 feeding! Like I said, we're amazed at the results.
Best of luck to you! I hope you find something that works well for you!