How long does it usually take a country to get over a recession? What factors influence the transition back to an economic boom?

This a very broad question. There is no "usual"  time frame for recovery from recession and transition to a stable economy.

. I expect you need to consider how the recession started and what led to it.  So it is dependant on the cause.

It could be war, it could be politics or it could be that the main product the country supplies the rest of the economy is no longer required, or not in-demand. Even the mood of the economy can be impacting (consumer confidence).

Supply and demand control the recession to Boom. ( the boom/bust  cycle). However policy, external influences and workforce also play their role in returning a country to a stable economy. or indeed causing a recession

For example if a country was mining and shipping "widgets", and it was in huge demand, for many years and then due to price pressure or demand it drys up, or the widget mine is mined out - then you have less income and no growth.

In most cases countries can forecast the advent of recession and are able to minimise the impact, to get out of recession - or avoid it - it can does usually take years, but in many case it could be a "blip" in the economy and recovery could haven over several months.