The U.S. Small Business Administration (SBA) is the federal government agency tasked with providing support to small businesses, including education, training, technical support, loans and grants (nonprofits only). The SBA does not provide direct grants to for-profit businesses for any purposes, including startups. However, the SBA does act as a conduit for other federal grant programs for small businesses and can connect small business owners with a wide variety of grant opportunities through its website.
Go to the SBA website (SBA.gov) and follow the links from the Loans & Grants page to Grants and then to either Research Grants for Small Businesses or Find Grants.
Research the types of grants that are currently available for startups in the area/industry of your new small business. Small businesses involved in technology research and development have a particularly good chance of finding a startup grant; as of 2011, as there are two multi-agency grant programs available -- the SBIR (Small Business Innovation Research) and the STTR (Small Business Technology Transfer) programs.
Create a list of grants that you think your new small business might qualify for. Narrow the list down to two or three of the most promising grants. You probably do not want to submit more than three grant applications in a short period of time to avoid reducing the quality of all of the applications.
Complete the application carefully and make sure to submit all requested supporting documentation. The length of time before you receive a response will vary according to the grant/agency, but 30 to 60 days is pretty much the minimum.