How can a person make his own engagement ring?

It would be easier and cheaper for you to design and order a customised engagement ring from a jewellery maker like Ingle and Rhode, or Diamond Manufacturers, or contract a professional to do so for you. It is a delicate procedure, but can be learned with time and money, through becoming an apprentice, or extensive reading on the topic starting with books like Make Your Own Rings and The Complete Jewelry Making Course by Jings McGrath.