You are a single person and you own the LLC as a member.
You put in the owners social-security number rather than the LLC's FID number.
Write in the name of the owner in the "Name" section and fill in the name of the business on the "Business" name section.
If the LLC is owned by a single member, you would have to put in the tax classification of the owner. If one LLC is owned by another LLC then put in the tax classification of the parent LLC and add a check mark to the LLC box.
If you are subject to backup withholding then before you submit the form you have to look to the Certification section and cross out the second section of three lines that starts with:
2. I am not subject to backup withholding.....
Read the form's instructions covering the areas that are being worked on. This will keep the details in check. Fill out the W9 form as an LLC more than once and you will find it easier to deal with.