Quick glance

CMS 17: in the US and US intervention (noun and adjective)

CMS 16: in the United States (noun) but US intervention (adjective)

Note: Some publishers prefer U.S. with periods.

AP: in the U.S., and U.S. intervention but US in headlines

Deeper details

Chicago style

Spell out United States as a noun, do not abbreviate—in the United States
Abbreviate US as an adjective, preferably don’t spell out—US intervention

Update! CMS has a new rule starting September 2017.

Now you may use US as a noun or adjective—

in the US
US intervention

(Source: CMS 2017, due out in September.)

Note: Some publishers prefer U.S. with periods.
And some may prefer to stick to Chicago’s former rule.

AP style

In text: U.S. with periods as a noun or adjective. The abbreviation is acceptable in all instances.
In headlines: US with no periods.
USA is fine when called for (but usually U.S. will suffice).
United States is usually only spelled out when part of a proper name or quote.

Chicago and AP agree

All forms take singular verbs:
The United States is, the U.S. is, the USA is (not are)

Possessive form

the United States’ farms*   the U.S.’s farms

*Because it’s a plural acting as a singular. Same situation with “plural” cities and companies: North Hills’ mayor, United Airlines’ flights. Not to be confused with a proper noun merely ending in s such as Kansas, which has different rules. See Plurals and Possessives of Names.

Sources:

Chicago Manual of Style 16   AP Stylebook 2016
Chicago Style dictionary is Merriam Webster’s Collegiate Dictionary, Eleventh Edition (MW11)
AP Style dictionary is Webster’s New World Collegiate Dictionary, Fifth Edition (WNW5)