You're not alone -- what you describe is extremely common. Babies like yours tend to be particularly sensitive to the noises, lights, and other sensory stimulation around them. When your baby is in your arms, she's more protected from this outside stimulation and less likely to wake up. Being held also prevents her from startling, a newborn reflex that causes her arms and legs to flail, which is another cause of wakening. Moreover, 1-month-olds are still adjusting to life outside the cozy womb. Being snuggled in your arms is much more like being nestled in your belly than sleeping alone in the crib.
The first step to getting your child to sleep is to carefully watch for signs of fatigue and to put her down at that time. Many parents decide to keep their baby awake and play longer, hoping then she'll get really tired and fall into a deep sleep -- a big mistake. Children who are overtired actually have a harder time getting and staying asleep. Next, if your child is sleeping in a crib, try a bassinet, as it's cozier and more comforting for a tiny baby. Swaddling -- wrapping baby up in a blanket like a burrito -- is also soothing and prevents babies from startling.
Once you put your baby down, don't rescue her too quickly. If she awakens and cries, pat her tummy or talk to her soothingly before picking her up. If that doesn't work, it's okay to let her cry for five to 10 minutes to let off some steam and soothe herself (as long as you're sure there's nothing else bothering her, like a dirty diaper or being hungry). If this fails, pick her up, rock her, and then try to put her down again. While you soothe her, stay in her room but don't turn on the lights or talk to her, as this is likely to arouse her.
If these tricks don't work, don't worry. Many babies this age need to be held to fall asleep, and that's fine for now. After 4 months, your baby will be better able to soothe herself, and you can train her to nod off on her own.
Originally published in American Baby magazine, November 2004. Updated 2009.