How do I go about starting an online lingerie business?

Having been there and done that I can speak from experience.

You will need to apply for a tax ID # from your state. You can use your SS# if you like.

You can set up accounts with lingerie manufacturers who sell wholesale and either buy in bulk from them or per piece. Many no longer drop ship so taking orders without existing inventory may become a problem.
Many allow you to use their model pictures so that is a plus.

You will need to set up an account to take credit cards /debits/checks over the internet.
Contact a company or your bank to purchase /rent a pos system and set up a business account.

If you do not know how to create a professional website you will have to hire an individual or company to create one. There is software out there to help create your own or online services you can purchase.
You will be paying a monthly fee to have this website on a search engine. Check into Yahoo. They get great results.

Good Luck with your endeavors

Competition is Very Stiff in this business

You may choose ebay..
Ebay.. the name spell success. It is a big business having multi billions dollars of tranaction happening in a year. There are countless person having a earning of 6 figure income. And of course many others having a regular income varying netween $500-$5000 per month. There are many persons, who has taken up this as a career but dropped it because they did not feel as an opportunity due to some or the other reason. There are certain guidelines which need to be followed to be successful in ebay like other business demands.For details visit
http://ebaysimplified.blogspot.com