Changing domain name

Consulted some “experts” and the way they communicate seems as though they have as much idea as me…

I have a domain/hosting situated at one provider, which as been online and live for a year.

My new domain which I want to replace the old one with is at another registrar.

I want to do a 301 redirect, so that my new domain name appears in the url of the old. However when I did the “change of address” feature in google web master tools didn’t work, I was told it’s because the files need to be migrated.

Does anyone know the most efficient solution?