The service you were in would have issued you the letter and placed it on your Military Record.
In order to obtain a Certificate of Eligibility for a VA Home loan, you will have to apply through the VA site:
This page has the following information on the page.
Eligibility requirements for a VA home loan program:
Learn about VA home loan eligibility requirements for a VA direct or VA-backed loan. Find out how to apply for a Certificate of Eligibility (COE) to show your lender that you qualify based on your service history and duty status. Keep in mind that for a VA-backed home loan, you’ll also need to meet your lender’s credit and income loan requirements to receive financing.
If you work with a lender that deals with VA approved loans generally they have VA home loan paper work that is filled out by the veteran seeking a home loan. This is called (COA) or Certificate of Eligibility. In most cases all that is asked for is for you to provide the lender with your discharge papers. I also know you can apply directly for a COA through the VA web portal ebenfits. Hope this helps. My recommendation find a VA approved lender.