The most important tool is your camera. If you have an older camera then its not as likely that you can get nice close ups. That doesn't mean a new camera has to cost hundreds of dollars though. I have a Canon Powershot SD750, it was about $230 at Staples, but you can get it a little cheaper on Amazon or Curcut City. My mothers camera is a Polariod i733 however and it takes just at great photos but you can get it on sale at Target for $80-$90, it just has less hoo hahs and doo dads.
The second most important feature is the Macro setting. This is usually marked on your camera with a little flower (see above). The Macro setting allows you to focus on close up images without them getting blurry, and it will lower the flash so things don't get washed out. My camera has the normal macro setting, and what I call the Super Macro setting. I use the normal one for full face photos and various make up photos, and the super macro for my eye close ups.
The super macro setting has no flash at all, so good natural lighting is a must. Luckly for me, I have five windows in my bedroom, so unless its overcast natural light is in abundance. I stand infront of the window that usually lets in the most light with the curtains closed so I don't have the sun glaring at me. I use a small hand held mirror behind the camera so I can see the view screen.
I rarely get a great shot without taking 5-10 photos first. Without the flash you have to be very still or else the photo will be blurry and my arms tend to shake a bit. After I think I've gotten a good shot, I take the photo to photoshop CS and crop, resize, and fix the color if I need to. Also I've found that its good to find the perfect angle and stick to that each time. If you're moving around all the time its hard to consistantly get great photos.
I found my camera on this excellent website, it ranks all the different camera brands, and then the cameras within each brand. Plus, you get to see first hand tons of photos that people have taken with each camera. Its so so helpful.
Hope that helps, thanks for reading.