New charities are created every day. The process is not difficult, but incredibly important. First, a new charity needs to become classified as an exempt organization by the federal government. This is key because it allows the organization to count any donations as tax-deductible, which is important because many donors give in part for the tax benefits.
A charity that the government has deemed an official nonprofit organization also has more credibility, which is an important consideration for potential donors. The IRS has a wealth of information which can help a fledgling group gain this exempt status and then start its life as a charity doing the good work that needs to be done.
First, when organizing a charity, develop organizing documents. There also are numerous attorneys who specialize in helping to file for exempt status. You can also check with your state (usually the Secretary of State office) for guidance. Many states have their own requirements.
Second, set up a board of directors. Don't have your board be made up entirely of family members, even if it's going to be a family-run nonprofit. Ask someone from outside your circle of friends to sit on your board -- someone with expertise in charities. This person can be vital in providing important, neutral advice. Also, consider either using your board as a way to bring in potential donors to the organization, or consider setting up an advisory board of high-level potential donors or rainmakers.
If you plan on hiring employees, then make sure to research what these positions pay. The National Center for Charitable Statistics often provides figures along those lines. It's also a good idea to solicit the volunteer help of a human resources manager for what to do (and not to do) during the hiring process.
Finally, set out discrete programs that you can accomplish in the next year. Use the development of those programs as a way to raise the profile of your organization and get off the ground.