the meditation you are talking about, simply focusing on your breathing, is a fine place to start.
you actually have the ability to shift your consciousness, almost instantly and in a near infinite amount of ways. for instance, you can be completely focused on your own thoughts. most intp's are inclined toward this focus, though normally no one is completely focused on any one thing. you can also be completely focused in your senses. this often happens if a dish falls and breaks, and in that sudden instant you are completely focused on the sensual world in order to take in as much information as possible in order to assess the danger (or more simply tring to figure out what the sound is). these are only two areas the consciousness can focus on, and they lie on the ends of a continuum between which your consciousness can focus whereever it pleases.
there are also the focus points where you are in a daze, just staring off into space.
a meditative state usually arises whenever you can completely enter into complete focus, or perhaps we could say meditative points, on any one end of the spectrum along which consciousness can move.
when you are focusing on your breathing you are trying to enter that focus point where your consciousness is only aware of your body. you are not aware of anythoughts in your head, in fact it will feel subjectively as though you don't even know what it means to be in the mind. everything that exists will be your body, lying or sitting or whatever, breathing, heart beating. when you reach this state, you are meditating.
you can of course also meditate by entering completely into thought and completely forgeting the external world.
there is also transcendental meditation, or spiritual meditation, where you focus upon nothing. well somepeople focus on nothing, such as the budhists. i never have very profound meditations when i focus on nothing. my strongest meditative states have came when i try to focus on God. it is sort of like focusing on nothing because we have no real concept of God, but it is a nothingness that is focused upward, or outward, or toward a higher spiritual being. hard to explain. this is the most difficult meditation. if you say to yourself, i am going to think about nothing, and then you immediately set out to do it, then at least for a time, no matter how short, you will be thinking about nothing. but outside thoughts will creep in easily. meditation is learning how to extend the time when you are thinking about nothing. eventually you will learn to focus completely on the nothing, just as above you were completely focused in your body, or in your mind. this is actually just the beginning stage of spiritual meditation. there are many levels which you can rise up to in such a meditative state that equals different levels of illumination, or transcendence. the first few levels sort of feel like just having a general sense of wonderment, but the wonderment is all you know. as the level and the intensity of the meditative state rises the wonder becomes absolute awe. at the highest level (at least the highest level i know of, i can't really imagine a higher level) feels as though you are suddenly capable of contemplating infinity. this is really difficult to explain, but this is experience can be very profound and life changing. i will admit that i have had this level of meditation a few times, probably three or four, and all of these were fairly close together except one. i can honestly say each experience altered who i was as a person. some people will become mystics and they will continue to have these experiences throughout their life. mine seemed to come for a time but i have not been able to reproduce them for a long time.
well i really rambled on there, but maybe this will help.