In Japanese, conjugation is fundamental to piecing words together with auxiliaries. For example, to express the polite past, we must first take the "ren'yōkei", or "continuative", conjugation of a given verb and attach it to the auxiliary ます (masu). When we do this with a verb such as のむ (nomu), it becomes のみます (nomimasu), at first. This is the polite form, as ます forms the polite. To properly express the polite past in full, we must add the auxiliary た. The stem of ます (masu) is a simple "mas-" sound. Since it ends with an S sound, a change occurs when we attempt to add た. The resulting "masta" is difficult to pronounce and not easy to write in Japanese, as it neglects the common consonant-vowel spelling rule. So, a compromise is made, also known as an 音便 (onbin), or, literally, a "sound convenience". The "masta" takes on an I sound between the stem's end and the auxiliary's beginning. Since there is no "si" in Japanese, "shi" is used instead. The resulting conjugation is のみました (nomimashita). When pronounced, it may be contracted and read as "nomimash'ta".
Source: tatoeba (12652385)