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First of all, in general, consumption of non-veg food items, by all people, under all circumstances is not a sin that scriptures will prescribe atonement measures for the act.

As clearly said in the following verse, giving up meat eating is greatly rewarding and is recommended too, but eating meat is "not that bad".

Manu Smriti 5.56. There is no sin in eating meat, in (drinking) spirituous liquor, and in carnal intercourse, for that is the natural way of created beings, but abstention brings great rewards.

However, this should not be understood as scriptures allowing unrestricted consumption of meat. Generally speaking, only sacrificial meat (i.e meat which is already offered to the Manes or the Gods first) is allowed (or recommended) to be eaten.

Manu Smriti 5.32. He who eats meat, when he honours the gods and manes, commits no sin, whether he has bought it, or himself has killed (the animal), or has received it as a present from others.

In general, one can do like given in the following verse once he realizes that he has taken something forbidden:

Manu Smriti 11.160. He who desires to be pure, must not eat forbidden food, and must vomit up such as he has eaten unintentionally, or quickly atone for it by (various) means of purification.

Also, for unintentional crimes, in general, the remedy is recitation of Vedic mantras. For intentional ones, atonement involves more severe penances that involve fasting for many days (like Chandrayana, Samtapana, Tapta Krikkhara, Prajapatya etc).

Manu Smriti 11.46. A sin unintentionally committed is expiated by the recitation of Vedic texts, but that which (men) in their folly commit intentionally, by various (special) penances.

So, again, it depends on whether one is initiated into the Vedas or not. If he is, then he can recite Vedic mantras like the Gayatri, which is known to clear all sort of sins.

Being clad in a pure cloth, seated on the ground and on a pure spot, and self-restrained, and by performing the achamanam with a pure hand, one should begin the recitation of the Gayatri. (212)

By the recitation of the Gayatri, all the sins, both of this world and of another, are dissipated in five nights. (213)

There is no purification of iniquitous deeds superior to the Gayatri. (214)

Verses from Samvarta Smriti.

Anyways, few penances are as follows:

Manu Smriti 11.152. But he who has eaten the food of men, whose food must not be eaten, or the leavings of women and Sudras, or forbidden flesh, shall drink barley (-gruel) during seven (days and) nights.

Manu Smriti 11.156. The atonement for partaking of (the meat of) carnivorous animals, of pigs, of camels, of cocks, of crows, of donkeys, and of human flesh, is a Tapta Krikkhra (penance)

For Sudras (one who's not wearing the sacred thread), however, the only remedy prescribed in scriptures is charity. The other atonement measures are not prescribed for him in the Smritis.

Source: 
https://hinduism.stackexchange.com/a/20584/13244