For https:// URIs, the client and server agree on which version to use as part of the TLS negotiation. For http:// URIs, major browsers won't be using HTTP/2 at all, but if they did, the spec defines a mechanism similar to websockets: the client makes an HTTP/1.1 request with a special Upgrade header, and the server responds by changing protocols in a coordinated way.
At the protocol level, this is covered by section 3 of the HTTP/2 spec: http://http2.github.io/http2-spec/index.html#starting
For https:// URIs, the client and server agree on which version to use as part of the TLS negotiation. For http:// URIs, major browsers won't be using HTTP/2 at all, but if they did, the spec defines a mechanism similar to websockets: the client makes an HTTP/1.1 request with a special Upgrade header, and the server responds by changing protocols in a coordinated way.