Anno Domini is Latin, conventionally translated into English as "in the year of the Lord." The conventional abbreviation is AD; periods after each letter are an optional matter of style, but modern usage dislikes them.
AD is sometimes misinterpreted as being an abbreviation for "after death," referring specifically to the death of Jesus Christ. This causes the common confusion resulting from the general consensus is that Jesus died roughly AD 32.
Convention requires that the letters be before the year, e.g., AD 800. Usage of "AD" in full dates, e.g., "AD July 4, 1776" or "July 4, AD 1776" is rarely enountered, and calls attention to itself, and on these grounds alone should be eschewed. For most AD-era dates, convention allows you to omit the indication that this is not in the era Before Christ. For three-digit AD-dates, however, there there is a greater tendency to use the form. You can say "the first Council of Nicaea was convened AD 325", and forms such as "the first Council convened in the early 4th century AD" are unexceptionable.
Contrariwise, BC is an English abbreviationism meaning "Before Christ" and ALWAYS is the last element. If the context does not otherwise indicate we are in such times, one is obligated to use the form. One can use it with full explicit dates, e.g., "Julius Caesar was killed March 15, 44 BC".