One of the most common and important tools to maintain the low inflation is the monetary policy. The UK, for example, the Bank of England sets their contractionary monetary policy by the aptly named Monetary Policy Committee (MPC). Then the government gives them an inflation target. Thus, the MPC will use the interest rates in order to try and bring the inflation to the target.
With an increase in interest rates, growth of the aggregate demand (AD) will slow down in the economy, slower growth leading to lower inflation as a whole since the higher interest rates reduce the overall spending of consumer. Why? Higher interest rates raise the cost of borrowing, so consumers are discouraged from spending and borrowing. Then saving money is now much more attractive. With the increased interest rates, people with mortgages or similar loans would have effectively lowered disposable income and consume less. The raised interest rates mean higher exchange rate value, meaning more cheaper foreign currency for the locals and a domestic currency becomes more expensive for the foreigner. This results in more imports to lower exports. As such, the slowing down of the economy by higher interest rates leads to lower inflation for all.