Most of these questions can be easily answered with a google search, but many people here should have plenty of information for you.
Breathing meditation is probably the most simple way to start. You simply relax somewhere comfortable, sitting or lying down, then you become aware of your breathing, as you breath in, gently feel the air enter your nose, and gently follow it as you exhale. You can count each breath if you'd like. In-out 1, in-out 2, and so on until you reach 10, then start again at 1.
Once you become aware that your attention has shifted to something else, other than following your breath, gently go back to the exercise above.. try this for 5 minutes or so a day. I would recommend starting with this meditation, and then moving on to chanting, but it's up to you. It's really about relaxation, focus, attention and concentration. Breath and chants are exactly the same. It's a preference.
I hope you find what your looking for, and I wish you luck on your search.
"We know nothing at all. All our knowledge is but the knowledge of schoolchildren. The real nature of things we shall never know." - Albert Einstein
"When will our consciences grow so tender that we will act to prevent human misery rather than avenge it?"