The classical approach is to do nothing and to rely on the natural robustness of the macroeconomy to solve the problem. Most macroeconomists agree that this is ineffective if not stupid, but it was first thought to be the solution to the 1929 market crash.
The Keynesian approach takes several forms but all of them are supposed to result in the so called "multiplier effect" causing the economy to grow once it has been stimulated by making more money available at some place in the social system. Unfortunately it doesn't work due to this money having to be borrowed or taken from some other part of the system. Keynesian economics is only a partial model and is unable to really show how it might grow.
The current Keynesian methods in use are to borrow money from the public and increase the national debt. Also to print more money and use it to reduce this debt, but this means inflation, and it is no more effective that that of the greater loans. Inflation is also dishonnest because it makes the debt owed by the government of smaller value in terms of what its money can buy. Money is only a representitive of wealth, not wealth itself. If the system were one of barter and in the present crisis then more money does not mean more wealth, except for the printers of course.
To reduce the rate of interest on the national debt does help to reduce the budget deficit for the next year, but it is not very effective and will not solve the problem at anything like the speed needed. So I find that with present methods there is no way to get out of the recession.
P.S. There is one way not yet considered, for which some essential reading is due (see references). It necessitates a reform of taxes so that land speculation is stopped and greater opportunities for work are created by the unrestricted acces to land.
"Progress and Poverty" (1879) by Henry George, published by the Schelinbach Foundation today. Also check the web for "Ask Henry" and www.progress.org etc.