Most descriptions of awakening are very general:
"With his mind thus concentrated, purified, and bright, unblemished, free from defects, pliant, malleable, steady, and attained to imperturbability, the monk directs and inclines it to the knowledge of the ending of the mental fermentations. He discerns, as it has come to be, that 'This is stress... This is the origination of stress... This is the cessation of stress... This is the way leading to the cessation of stress... These are mental fermentations... This is the origination of fermentations... This is the cessation of fermentations... This is the way leading to the cessation of fermentations.'http://www.accesstoinsight.org/tipitaka ... .than.html
The most detailed description of actual technique is probably the Anapanasati suttas such as the one culaavuso mentions above. However, there are many meditation objects described in suttas such as Satipatthana Sutta
"And what is the development of concentration that, when developed & pursued, leads to the ending of the effluents? There is the case where a monk remains focused on arising & falling away with reference to the five clinging-aggregates: 'Such is form, such its origination, such its passing away. Such is feeling, such its origination, such its passing away. Such is perception, such its origination, such its passing away. Such are fabrications, such their origination, such their passing away. Such is consciousness, such its origination, such its disappearance.' This is the development of concentration that, when developed & pursued, leads to the ending of the effluents.http://www.accesstoinsight.org/tipitaka ... .than.html
My impression is that particular objects, such as breath, are not the point. The point is seeing characteristics and processes such as anicca, dukkha, anatta, and the various permutations of dependent origination. Objects such as the breath, and the various objects in the Satipatthana Sutta and others seem to be just particular examples.
However, I do sometimes see statements to the effect that anapanasati was the method that the Buddha used on the eve of his awakening. I would be interested to see a sutta reference for that. Various suttas describing the Buddha's awakening are given in In the Buddha's Words, Section II.3
, but I see no mention of anapanasati in those.