There is a major contrast between the British and American changes of government. In the UK a General Election is held between the hours of 7am and 10pm, in recent history - on a Thursday. Once the polls are closed the ballot papers are counted in each constituency and results announced. In most modern elections the "winning party" is known by the early hours of the day following the election. If the result involves a change of Government - the existing Prime Minister will resign that day and the Queen appoint the new PM on that day. The new administration starts work immediately.
In the USA there is a transition period. Originally the new President took office on 4th March - which could be over 4 months after the election, but this was changed by 20th Amendment to 20th January.