The idea behind the lowering of interest rates, first to below 1% and now to the targeted 0% is that it will make it easier for banks to get money and then to lend it out, and since our economy runs on credit rather than cash, this is supposed to be a good thing.
The only problem is that it makes it very easy for banks to get money but not quite so easy for others to take that money. Banks are, not surprisingly, a little gun-shy given all the defaults and other bad loans around, but the issue is that the incredibly low interest rates discourage saving and in some ways discourage investment of real capital. This is not good in the long run and may in fact lead to serious and very problematic inflation.
Members of the United States' government would certainly argue that they have attempted to alleviate the effects of the recession. They would cite the bank bailout (under President Bush) and more recently the stimulus package, homebuyers' tax credit, and automotive bailout as examples of their being proactive in addressing the recession.
The Fed has consistently dropped interest rates over the past several years, and mortgage rates are the lowest that they've been since the 1960s.
With all that being said, each person has his or her own opinion regarding whether the government's actions have helped us out of the recession. You have to look at unemployment rates, foreclosures, the stock market, etc., to determine what you think.
If you are talking about the US government, they have done a number of different things to try to get us out of the recession.
With regard to monetary policy, the have tried to keep the money supply relatively high. They have done this, in part, by keeping interest rates very low. They have resisted the idea that they might raise them out of fear of inflation.
With regard to fiscal policy, the government has done a lot of extra spending to try to stimulate the economy. They have created various stimulus packages to try to pump more money into the economy, for example. They have also extended the amount of time that people are able to get unemployment benefits.
Finally, the government has created programs (like the cash for clunkers program) that are subsidies and are meant to lower the prices that consumers have to pay for things like cars.