I am a student currently working for a U.S. company on my OPT. How soon should I contact my company to apply for an H-1B on my behalf?

As soon as possible. USCIS will start accepting filings of new H-1B petition on April 1, 2015. Your company and attorney need ample time to assess your case, gather the necessary documentation, and prepare the petition. If you are seeking to change your status to H-1B and are subject to the April 1 deadline, contact your employer in advance.