I have been doing some contracting work and the company has asked me for my 1099. How do I go about getting that?

More than likely the company you are doing contract work for (which means you're self-employed) asked for a W-9, not a 1099 of any type. You can print a blank one at https://www.irs.gov/pub/irs-pdf/fw9.pdf then fill it out and provide it to the person or entity that will be paying you.

If you have an EIN, then provide them your EIN and not your SSN.

If you don't have an EIN and would prefer not to provide your SSN, then you can obtain an EIN absolutely free in about 10 minutes at https://www.irs.gov/businesses/small-businesses-self-employed/apply-for-an-employer-identification-number-ein-online

Actually, the company gives you a 1099-NEC for the money they paid you for the work you did, like an employer gives you a W-2.  Most likely the company is asking you to fill out a W-9 form for them.  See:

Form W-9 (Rev. October 2018) (irs.gov)

Forms and Associated Taxes for Independent Contractors | Internal Revenue Service (irs.gov)