First and foremost, you must have a D-U-N-S number from D&B Inc. This is a number unique to your business entity that serves as a way for Apple (and other organizations) to identify your business.
Getting a new D-U-N-S number can take 30-45 days for normal registration via D&B's site but you can speed up this process for an extra fee if you register via this link, it only takes 5-7 business days.
However, if you already have a legal entity for your business, you may already have this number and not know it. This may not work for brand-new legal entities, but you can search the D&B Business Directory for your entities legal name and request to receive an email with your DUNS number for free. You can also search your company/organization name via Apple D-U-N-S Number Lookup site and (if needed) request a D-U-N-S number for it.
Once you get the D-U-N-S number, you can use it to fill out Apple's Individual to Organization Membership Update form to request that your individual account be changed to a company/organization account. This is different from the "Enterprise" tier, which costs more money and is intended for businesses that need to privately distribute apps outside of the App Store.