In the United States, redistribution, to the extent that it exists, is accomplished through fiscal policy. Much of the redistribution is through entitlement programs. Fiscal policy is policy that has to do with taxation and government spending. The federal government accomplishes some redistribution through its progressive income tax system. In this system, people with higher incomes pay higher tax rates and people with lower incomes often receive more money from the government than they paid in taxes. Redistribution also happens through things like the Medicaid system, in which poorer people get health care benefits that are largely paid for by the taxes that wealthier people pay.
The effectiveness of the redistribution system in the US is the subject of great debate. Conservatives tend to point to the fact that the poverty rate has not declined much in the US even as the welfare state has expanded. Liberals argue that the poverty rate does not take into account government transfers that poorer people get that make them much less poor than their actual incomes would indicate. Conservatives also argue that the redistribution system hurts our economy because it imposes disincentives for work on the wealthier people in the form of higher taxes.
Does this process make the US more of a socialist country than a capitalist country? Redistribution is certainly something that would happen in a socialist country and would not happen in a country that is purely capitalist. However, socialism and capitalism are two points on a continuum, not separate categories with clear dividing lines between them. The fact that we have some redistributive programs moves us away from pure capitalism and towards socialism, but it does not mean that the US is a socialist country.
Redistribution, then, is accomplished largely through fiscal policy that is driven by a progressive income tax. Redistribution does move the US away from pure capitalism on the economic continuum, but it would be hyperbolic to say that the US is a socialist country because we have things like a progressive tax structure and Medicaid.