It's meditation and practising the things learned in meditation. First it's getting to know how the mind works, and observing our motivations. You would focus on somthing that needs improving like anger, as an obvious one. It's not easy, but by meditating upon the harm anger causes and then the antidote - patience - you gradually become more aware of what happening to you when you become angry, and the idea is to snuff it out before it takes a hold. As we all know, anger is very difficult to control, but meditation gives you a little bit of reflective space to try to control it.
This is just the beginning though. Once you've improved your self control, then you begin to try to improve you kindness and compassion. It seems a little artificial at first, but with practice, it becomes a more genuine experience. It's based upon the idea that the mind is not a static, unmoving thing, otherwise there would be no possibility of improving one's mind, but is constantly changing. My friend has been a longstanding practitioner, and I have noticed the change in him.
This is merely the tip of the iceberg though. The way I've put it is very matter of fact, but there is a spiritual element to it as well - offerings, prayers and mantras as you said. I'm not very familiar with Hindu methods though.
