If your company will like to cooperate, then you can do it by yourself and send in to go through premium process, it will just take around 7-10 days to finish, the max is two weeks.
Google the H-1B check list:
And let your company provide tax number and related tax information and revenue information, and fill I-129, I-129w, and submit your copy of all related Ins documentation like I-94 (FRONT AND BACK ON SAME PAGE), passport, visa, i-20, Offer letter, resume, and read the form instruction carefully. Good luck.