interest rate

I am assuming you are taking about Central bank in a country

In short, to lower IR, increase money supply by purchasing government securities on the open market. It's all just the basic Supply and Demand, more supply, less expensive to borrow.

Take US as an example: (basically the same for most market economy)
http://en.wikipedia.org/wiki/Interest#Open_market_operations_in_the_United_States

How will it affect the economy? Same for market economy like US/Canada

In the simplest form, discourage savings and encourage lending, thus, demand for many things will increase, prices increase --> higher inflation

by lower IR, the govt is probably taking an Expansionary_monetary_policy:
http://en.wikipedia.org/wiki/Expansionary_monetary_policy

Other than prices, it's hard to say:
(wiki)
Neoclassical and Keynesian economics significantly differ on the effects and effectiveness of monetary policy on influencing the real economy; there is no clear consensus on how monetary policy affects real economic variables (aggregate output or income, employment). Both economic schools accept that monetary policy affects monetary variables (price levels, interest rates).


You could discuss this topic in depth...but I hope this answers the basic questions.