How did a centrally planned economy influence economic growth in the former Soviet Union?
This is a complicated question difficult to reduce to a short answer and depends on the time period. But it's helpful to highlight some of the fundamentals of the former Soviet Union's centrally planned economy by viewing it through the lens of the collapse of the country in 1991.
The political climate, particularly the arms race of the 1980's, resulted in severe misallocation of resources by the central planners. Some economists estimate that more than 50% of the government budget in some years went towards production of arms, resulting in underinvestment in industrial goods needed for the rest of the economy. As a result of this underinvestment, shortages became more common and long lines of consumers looking for basic goods was frequent.
Central planning also resulted in low worker productivity. There were few incentives for workers to increase their productivity, a common critique of socialism/marxism. One Russian economist, investigating low productivity in Soviet mines, concluded that the workers had no incentives and
"The Soviet system is not working because the workers are not working"
In a very broad sense, the centrally planned economy resulted in economic growth that the government thought was most important: growth of the military-industrial complex. The result, as discussed in the first point above, was detrimental to other areas of the economy.
The government took complete control of the Soviet Union's economy. A new government department was set up to set targets in each industry, like what production each industry was supposed to reach. If it had been reached, there would be rewards given to the workers for their contribution, earning a higher salary. If it was not up-to-standard, they were punished or sacked from their jobs. This really limit work productivity as they are forced to follow targets, limiting their creativity, listening to the government's beck-and-call.
Many of the government's Five Year Plans were aimed at millitary production or heavy industries like the building of ammunition, steel and iron production, electricity, chemicals and engineering industries. Most of the government budget was focused on these targets, so less emphasis was placed in consumer production like clothing, so there is really poor working conditions for the workers. Salaries dropped by 50%, as they could buy less with the same amount of money.