My wife and I have used cloth diapers for our baby since he was 2 weeks old. Modern-fitted cotton diapers with Velcro and snap closures aren't the thin bits of cloth that your mom folded and pinned together. There are two layers: the cotton diaper, about a half-inch thick, and the waterproof nylon shell that goes over the outside and keeps all the waste inside.
The kind we use, Snug-to-Fit, fits babies of all sizes. The diapers' front portion folds down to fit newborns, and you unfold them for larger babies up to 35 lbs.
Over the two or so years that most babies spend in diapers, they can go through thousands of disposables, typically costing a couple of thousand dollars.
Handling cloth diapers is a snap, too. When we change the diaper, any solid waste gets shaken out in the toilet. The rest goes in our diaper pail, a five-gallon bucket with a liner. We snap down the lid to keep the smell in and remove the bag with the dirty diapers when it's full. Two washes and a drying later, and the diapers are back in service.
I believe cloth diapers are healthier, too, because your baby has natural fibers against his skin instead of plastics and because they force you to change the baby's diaper more often. Disposables can hold more urine, so they're typically left on longer and are more likely to cause diaper rash.
Greening your baby is a way to help your child become environmentally conscious right from the start and a chance to live out your values in a practical way.