Hi, einnoc! You've gotten some really great tips here. Thought I'd throw in my two cents since I used to take lots of photos, too, back when I had an Etsy shop.
I went the low-tech route - I read up on how to build a lightbox but was too intimidated to actually try to construct one.

So, I saved a sturdy medium-sized cardboard box, cut it up, and taped it together to make an easel. Then I clipped scrapbooking paper to the easel for my foreground/background.

I took my photos on the kitchen counter because that's where the light is the best for me. The kitchen is well-lit and there's a big sliding glass door nearby for natural light, too. That's what worked for me, but go wherever the light is best for you.
One thing that totally changed everything for me was when I discovered the EV compensation setting on my camera, which allows you to overexpose (brighten) or underexpose (darken) your photo. I don't know if your camera has a way to manipulate the exposure compensation, but check your user's manual to see. EV compensation is really handy if your photos are just coming out too bright or too dark - sometimes it's tough to fix that later in photo editing. Oh, and I never used a flash - the light from the flash is just too harsh and unnatural.
And I usually had to do some photo editing like tartchef does. I also adjusted the brightness and contrast and cropped my photos at the very least. I usually just used MS Office Picture Manager for that, but Picnik is a great (and free!) option, too.
I have a DSLR and I usually used that for my soap photos. A good point-and-shoot camera will take great photos, too, though. But I know what you mean about how it's easier to steady a camera when you have to look through the little opening because then you can kind of rest the camera on your face and bring your elbows into your chest to decrease shaking. Does your camera have a shake reduction setting? If not, I use the macro setting and rest my elbows or wrists on something when I take a photo with my point-and-shoot. Tripods are great, too, if you can get a good angle with them.
I hope that helps. Taking photos can be tricky and it takes practice. Good luck!