Well, there is no such thing as a "1099 employee." You can be an employee, or you can be an independent contractor. An independent contractor is a separate business (even if just one person) who provides services to other businesses. The business is your client, not your employer. There is some information here.
https://www.irs.gov/businesses/small-businesses-self-employed/independent-contractor-self-employed-o...
Whether you are an employee or independent contractor depends on your relationship, and who has control over the time, place and manner of work. For example, if you are an artist, and you are an independent contractor for ABC company, then you decide whether or not to accept assignments, how to perform them, and where to perform them. You can also accept assignments from other companies. If they tell you that you must work in their office and can't take assignments from other companies, you might be an employee. You might be legally considered an employee even if you signed an agreement to be a contractor, if the company is abusing the conditions of work.
If you are really an independent contractor, then you are a small business. You file a schedule C, to report your gross income, deduct any ordinary and necessary business expenses, and pay both income tax and self-employment tax on the net profit. The net income from schedule C flows to the rest of your tax return where it is combined with all your other income, credits and deductions. Other users here will give you links on how to file a schedule C.
If you think the employer is abusing the rules and you should be an employee, you can file a protest using form SS-8, and file your tax return as if you were an employee. This will be difficult if you signed a contract to be treated as an independent contractor, you would need substantial proof that the business is violating the rules.
