I suppose the answer to "How to get into digital photography?" really depends on where you are currently with respect to photography and where you want to be. If you just care to remove red-eye from your snapshots, then look toward basic post processing. If you're looking to take photos that makes people go "wow," then you'll first need to understand the basics of photography.
If your goal is the latter, just taking more and more snapshots with a point and shoot will just yield a lot of the same old photos anyone can take. You may get a good one here or there by chance, but at some point, you'll be disappointed that your photos don't come out the way you had envisioned it or doesn't compare to some of the beautiful shots of similar subjects you've seen online. So if you're not already there, to start, forget about the "digital" aspect of photography and just learn the principles of photography. Understand how aperture, shutter speed and ISO interact and the effects they create. Understand the rule-of-thirds and other composition techniques. Then learn post processing.
I actually got interested in photography after I saw some photos from a gf's friend's vacation and, interestingly enough, the photos from AT's virtualmike's website. I only owned an old 5-year old P&S at the time with no ability to tweak individual settings and I wasn't ready to drop money on a pricey SLR. So I just read up on the basics of photography without a camera. After a few months of picking stuff up here and there, I was itching to buy a camera to test it all out. I bought a Canon XTi with a 50mm F/1.8. At first, I was all giddy and starting taking a bunch of snapshots with disappointing results. I was wondering if there was an issue with my setup until I realized I wasn't applying the things I read. I slowly got better and I picked up some post processing to add additional pop to the photos. I'm much better at photography now, but still far, far, far from being able to take photos of the caliber of those some of our members.