Employment in the private sector is much less prescriptive than the federal or other government sectors. The most prominent obstacle you are likely to face will be in learning how to translate your experience in a way that makes you look attractive to a future employer. That means it is imperative that you do your research, understand the company, and pay particular attention to what a job description indicates the company is looking for – and targeting your resume for that specific position. Not an easy task – but in today's economy, only those whose resumes make it to the "top of the pile" will likely be the ones sought out for an interview.
While most companies will tell you to apply online, some companies provide additional assistance during the recruitment and application process for veterans.
Private industry is much more than "corporate America." It also includes nonprofit organizations and veteran service organizations – two industries often overlooked during the employment search.