What methods are used in agricultural practice for breeding animal breeds?

Selection is used. This is essentially artificial selection. The livestock breeder or breeder selects the best representatives of the animals and mates them. Further, the best representatives are again selected from the offspring for further breeding. Breeding may not always give the desired result. Nowadays genetic engineering is very developing, which gives the same results as selection, but much faster and safer. But if ordinary farmers themselves can engage in selection, then they will not be able to carry out genetic research in any way.