curl supports HTTP/2 for both HTTP:// and HTTPS:// URLs assuming that curl was built with the proper prerequisites. It will even default to using HTTP/2 when given a HTTPS URL since doing so implies no penalty and when curl is used with sites that do not support HTTP/2 the request will instead negotiate HTTP/1.1.
With HTTP:// URLs however, the upgrade to HTTP/2 is done with an Upgrade:
header that may cause an extra round-trip and perhaps even more troublesome, a
sizable share of old servers will return a 400 response when seeing such a
header.
It should also be noted that some (most?) servers that support HTTP/2 for
HTTP:// (which in itself is not all servers) will not acknowledge the
Upgrade: header on POST, for example.
To ask a server to use HTTP/2, just:
curl --http2 http://example.com/
If your curl does not support HTTP/2, that command line will return an error
saying so. Running curl -V will show if your version of curl supports it.
If you by some chance already know that your server speaks HTTP/2 (for example,
within your own controlled environment where you know exactly what runs in
your machines) you can shortcut the HTTP/2 "negotiation" with
--http2-prior-knowledge.
One of the primary features in the HTTP/2 protocol is the ability to multiplex several logical stream over the same physical connection. When using the curl command-line tool, you cannot take advantage of that cool feature since curl is doing all its network requests in a strictly serial manner, one after the next, with the second only ever starting once the previous one has ended.
Preferably, a future curl version will be enhanced to allow the use of this feature.