One of the things most beginners don't have and often don't think about is a tripod or camera support. So why do you need a tripod? Some think their hands are perfectly steady, and that the auto settings will get everything right, but a tripod will always get you better results.
Low light situations call for slower shutter speeds, even with point and shoot cameras that have an auto setting for night or museum (this generates a slower shutter speed and no flash) and a slower shutter speed will usually result in some camera shake blur, even with a steady hand. In this situation, a tripod is a "must have", so use a tripod.
For shooting fast paced action, like sports or motorcar racing a tripod can hinder or help, so you need to be sure you are using the right tripod. The same applies to any movement that you want to freeze - in general you need good lighting and a fast shutter speed, and usually good timing. If you don't have a tripod with a ball head, it's probably better to try it hand-held.
For landscape, waterscape, plant, flower and other nature photos, use a tripod.
When you are working in a 'studio' setting (indoors, sometimes even outdoors with gooding lighting and/or the option of setting up proper lighting) use a tripod - sure it takes a little more time to set up than just grabbing the camera and snapping, but you'll always get a sharper shot with the tripod.
If, like me, you like to walk with your camera then a monopod can be a handy thing to own. It helps to steady the camera a lot and is not as bulky as a tripod to carry around. Some monopods have a base that opens to three legs, and these are even steadier, but no more bulky than the others.
Other things you can use to steady the camera are bean bag supports, and if worse comes to worse a fencepost, tabletop or garbage can, but I prefer to use a tripod.
I currently own 4 tripods and one terrific monopod. One tripod is lightweight with the ability to hang the camera upside down for carrying with me when I need to, one is a medium weight with a ball head, one is a heavy duty old and clunky but very sturdy professional model, and one is a small table top model (not recommended for bigger camers unless you invest in a heavy one) - all have telescoping legs and two have bags (you can buy bags separately). The monopod has a ball head and quick release, telescoping leg and acts as a walking stick.
There are very few images or situations where I don't use a tripod or other camera support.
One thing to note - if you are using a lens or camera with image stabilization (or vibration reduction) it is probably better to turn off the IS/VR when using the tripod.
So if you don't own a tripod, now is the time to get one. The cost of a tripod can range from $30 to $1,000+. For everyday snapshot use you can probably get by with a tripod in the $70 price range, but if you plan to do anything else with your photography invest in the best one you can afford (I'd suggest starting somewhere in the $150-$200 range).
There are lots of places to buy or price camera supports. Two of the places I use are Vistek and Henry's Camera - mostly because I can get to either one in person (the furthest away is a 2 hour drive from me) or I can order over the internet and have them shipped, and because I've done business with both places and know that I can order safely from them. The third place I use is local, just down the street, however they don't have internet sales.