Riksbank Deputy Governor Karolina Ekholm gives a insightful speech on this topic:
She shows via examples how exchange rate changes leads to changes in inflation. It is via the import basket channel. If exchange rate depreciates imports become expensive, If imports form bulk of the inflation basket, it would lead to a rise in inflation.
Then she looks at how exchange rate impacts overall economy. Exchange rate depreciation leads to higher exports but it works with a lag. Usually trade deficit worsens after exchange rate depreciation and improves gradually.
She also looks at exchange rate forecasting explaining concepts of nominal & real exchange rates, interest rate parity and purchasing power parity. We can kind of predict exchange rates looking at current account and GDP growth rates but only over a long term.
Read the whole thing. Highly insightful. Makes a primer on exchange rates right away. One can keep this speech for future references. It is a topic central banks touch very rarely.