well, its not so much about just doing the breathing and hoping then that transcendence or even calm will necessarily descend upon you by default of your actions- it takes mental focus and strength, which has to be built up. the breathing helps focus your mind on a single point of interest, to the exclusion of all else- that's the primary reason for the emphasis on breathing in meditation. it brings the attention to yourself, and away from the world around you, your stresses and cares, the ear-worm song that's been playing in your head all day, etc.
but while the breathing helps in this, its not an automatic trigger kinda thing- you know, breath deep for a while and you'll find yourself in a transcendent state lol. meditation's power depends upon your ability to focus your mind for extended periods of time- not easy in today's culture where tv's effectively trained us to have 5 second attention spans (i'm not exagerating).
to get better at this, before even introducing special breathing techniques, try to just sit in a comfortable chair, close your eyes, and fix your mind on a single thought. say, for example, a pencil. hold the image of that pencil in your mind for as long as you can- imagine it's texture, its weight and feel in your hand, its scent, its colors, what's written on it? is the eraser chewed-on? is it sharpened? just keep rolling that single thought around in your mind making it as real as possible for yourself for as long as you can. the instant any other thought intrudes- what's for dinner? gotta do that homework later on.. i wonder if i'm doing this right... what about colored pencils? crap i forgot to schedule that doctors appointment- the instant another thought intrudes, stop, and then start again fresh. you'll find you have an attention span of like 20 seconds at first when trying really hard- it'll get better though. you also discover an interesting tendency of the mind- the harder you try to single out any single thought, the harder your other thoughts will try to interfere. the calmer you try to make you mind, the harder it will rebel. that's what breathing techniques help quell, because you have a steady, unending, rhythmic physical reality to ground you mind in, as an anchor- i still suggest working on just calming your mind first though before working at sustaining a calmed mind. meditation is an altered state of consciousness, not just simply being relaxed, as your brain actually slips into a pattern of brain-waves that are akin to sleep- except that you're still conscious. so it's important to understand what's happening and how to create that state before working too hard at the means of aiding that's state's creation- the breathing's a tool, essentially. once you get proficient at holding a single thought in your mind for, say, 10 minutes, i'd start working on trying to think of NOTHING for an extended period of time. THAT'S a hard one. its hard to think of nothing for more than a second or two before SOMETHING pops up. i imagine my mind as a vacuum like space, or as existing in a pre-formation, potentiality. a useful technique here to get started is imagining what your life and existence was like... BEFORE you were conceived! loose yourself in nothingness and try to consciously hold that state. when you're proficient at that, i'd incorporate breathing techniques to help lengthen and perpetuate that state, and to deepen it. you'll find time moves strangely when you're in that state, btw... because you're technically sleeping, and awake, and self-hypnotized, all at the same time- so while you're aware vaguely of being there in time and place, you'll come out of it after what feels like 15 minutes and it'll have been an hour! that's how you know you did it right.
once you get good at THAT- you can start using meditation for its intended use, as opposed to just using it to lower your blood-pressure and alleviate stress from your day. you can start using it to destroy, temporarily, your sense of self and to identify the self with EVERYTHING. this eventually results in a transcendent state that is impossible to describe. but it's better than any orgasm :p i haven't felt it yet but i know of it- it's definitely worth the effort.
btw, another useful technique to help learn to focus your mind: staring at a candle flame and thinking of nothing but that flame for as long as you can- imagining any stray thought in your mind being instantly incinerated in the flame of the candle, before it can even take form.
anyways, hope this helps