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As a disclaimer, I do not have experience in the industry.
Nevertheless, breaking into any industry falls under the same basic structure. To start, you need experience. My recommendations:
1) Internships - One of the best ways to gain experience. Seek out internships through websites, like internships.com, through company's career/employment pages on their websites, and through your own cold emailing (i.e. if the company's website doesn't list an internship available, you can still email them to tell them of your interest. It worked for me before).
2) Entry Level Job - You may learn more or less with this type of job. If you are looking to start your own, then target a small company. Working for a large company might take you longer to move around to see different areas of the organization.
3) Externships - If the top two fail for whatever reason, you can try for an "externship", i.e. job shadowing. These are likely to be one-day or short-term engagements, but they will allow you to see first hand the operations behind the business and network for future potential opportunities.
With that said, I recommend your next steps to be:
1) Locate and research local beauty companies in your area.
2)Write these down on a computer document or in a notebook.
3) Research some basics like what their products/services are, who their target market is, how long they have been in business, and any other notable facts.
4) Locate their employment section. If they are seeking an intern -- perfect! If not, find the email of the H.R. department or any contact within that department and email them of your interest. If you can't find that information, try to seek out the email of someone else at the company to start. Keep the emails short but intelligently written. Spell check and read it over twice before sending! Then you have a template for other companies as well.
Best wishes -- feel free to question me on anything else following this.
-David J. Bradley