You would issue a 1099-MISC if you are a business making payments of more than $600 per year to a person or sole proprietor. This could be someone who subcontracts for you or assists you on jobs. (You don't need to issue a 1099-MISC if you are making payments to a corporation in the corporate name, like your vendors for supplies and materials.)
If you are making payments to someone that requires you to issue a 1099, the deadline is January 31, 2018 for payments made in 2017. There are a variety of web sites that will allow you to e-file a 1099-MISC for a small fee (under $5) where one copy goes to the IRS and one copy to the person who received the payment. Turbotax has e-filing of 1099-MISC forms in the online and desktop versions of Turbotax Self-Employment, but you won't be able to use Turbotax to issue a 1099-MISC for 2017 until December.
I suspect your clients want to issue a 1099-MISC to you to report the payments they made to you for work you did for them. In that case, they are asking for a W-9 form, which you use to tell them your social security number or tax ID number so they can issue the 1099 to you.
https://www.irs.gov/forms-pubs/about-form-w9
If you don't have an EIN for your business, you may want to get one. You are required to have an EIN if you pay employees, but even if you don't have employees, you can get an EIN and that way, you give your clients your EIN instead of your personal SSN. You can obtain an EIN from the IRS web site in about 20 minutes.
https://www.irs.gov/businesses/small-businesses-self-employed/apply-for-an-employer-identification-n...
