I'm 18 years old and want to start taking pictures of my day-to-day life. I am aspiring to become a photographer for people and events, etc. I am keen to buy my first camera which is cheap, easy to understand and that can produce great quality and crisp images. Since I'm new to this I'm not quite sure what to look for. Any ideas?
Big subject. This and any other answer can only be an introduction.
You MUST define "cheap" as you see it.
Your lens will have an extremely major effect on the result. See below. A P&S can meet your spec but you really want a DSLR.
In high light situations some quite basic P&S cameras can work very well.
Do not be mislead by megapixel madness. More is usually better all else being equal, BUT all else is seldom equal and higher mp is often at expense of final quality.
You do not want a camera that is easy to understand - you just want a capable camera with a "bunny mode" that you can use until you get used to it. ALL well made cameras are easy to understand after a while - you just need a friendly learning mode.
Lenses that you will require depend on desired style etc. A mid range zoom is a desirable start. A 50mm or 35mm f/1.8 or better prime will be your great friend in due course but is not necessary initially - but if a good & cheap one wanders past, you want it.
Great quality is in very large part dependent on the part of the overall photo taking system that holds & owns the camera (ie = you, in case that wasn't clear :-) ).
To see what the specs of both new cameras and old lower mp models are like in practice look at a quality review site and pore over both samples and tests. I recommend the superb DPReview site , but there are many others.
Depending on budget, I'd start by looking at:
If "as cheap as possible" is the aim, reviews etc for 6mp range DSLR's which are available at good prices second hand.
If somewhat more money is available, one of the entry level cameras that has good reviews in the areas that interest you. Note that the DPReview tests and those of all good sites provide sample images taken under a range of conditions. Look especially at the ones that reflect you areas of interest. In my case, I am biased towards cameras that both
ie gigs and shows, & street at night, motocross, surfing, athletics ... . The two apparently different requirements converge because you need low noise at high ISO for low light photos and you need the ability to use high ISO for action shots so your shutter speeds can be fast. Others are biased towards great dynamic range or awesome colour rendition or ... . .Everything matters, but wht matters most to you needs optimising when you make decisions.
Added from a comment elsewhere:
@weberc2 mentions Nikon & Canon 50mm f/1.8 lenses.
Sony make a similar 50mm f/1.8 lens.
I think we all want a camera like that.
Your first decision is whether you want a DSLR, or a pocket sized camera.
If you want DSLR, you can't go far wrong with a Canon EOS or a Nikon. The EOS1100D is the entry level and is around the same price as a pocket-sized point-and-shoot. It is a bit basic and plasticky, but works well enough and lets you change lenses. The Nikon D3100 is very similar.
For a pocket camera, I have a Canon PowerShot as my 'spare' and have no real complaints about it, other than the standard ones that apply to all that style of camera: poor low light performance, slow reactions, noisy output, etc. As long as you stick to known names you can't really go far wrong in that class.
There are also some oddities. The Nikon Coolpix range that are the size of a DSLR but have no interchangeable lenses, or the Sony NEX that have a decent size sensor and interchangeable lenses but are not SLR.
Whether you view these as the best of both worlds, or as neither one thing nor the other, is really a matter of opinion. Myself... I would say that for the price of a Sony NEX, you can buy a Canon EOS 600D which is a far better camera.
This is only intended to supplement the previous answers, but I've had a great learning experience with a cheap, used, 2004 Canon 20D--it doesn't have all the bells and whistles of newer models, which helped me to learn the basic dynamics of photography. Also, Canon and Nikon both have $100(US) 50mm 1.8f lenses that work great in low light, and they don't zoom so you learn to shoot with a prime lens. They're not great quality, but the value can't be beaten. A setup like this (and perhaps some sort of 18mm-200mm zoom lens to practice other types of shots) should get you well on your way to learning.
Also, before I bought a camera, I spent a lot of time looking at photos I liked, studying why I liked them, and searching the Internet for how to produce those effects with a camera. In doing so, I came to learn a lot about the various technical photographic properties and their impact on photos. This helped me pick components that worked well for the styles I wanted to learn.
If you want to be a pro photographer you need a DSLR and you need to learn how to use it, if you are planning to be a serious hobbyist you can make do with a point and shoot but you still need to learn the technical side of photography (and I still suggest a DSLR).
The good news is that those cameras with their million little buttons, knobs and dials are actually very easy to understand and use after you learn the basics (and they always have an auto mode you can use until you learn) also the most basic DSLR with the kit lens will give you better image quality than almost any point and shoot.
The biggest downsides of DSLRs is that they don't fit in your pocket and that all the lenses and accessories are expensive.
On the other hand, if you only want to take pictures of your day to day life and you don't want to learn the technical side of photography a good point and shoot may be a better choice - they are small and very easy to use.
The biggest difference between a point and shoot and a DSLR is control - with a DSLR you can control exactly how the picture turns out, this is not only due to the camera features but also because of the bigger lens and sensor, effects that are difficult or impossible with a small point and shoot and easy with a DSLR (like blurring the background).
If you go for a DSLR you really can't go wrong, even the entry level DSLRs are great (the biggest companies in this field are Canon and Nikon, if you go with one of them life will be easier in the future when you look for lenses and accessories)
If you go for a point and shoot every recent camera from an actual camera company will be good enough, you have to choose a model based on the tradeoffs between size, quality and price.