I recently read Richard Storry's A History of Modern Japan (1960), so I can answer for Japan. The Naval Treaty had a ratio on allowed capital ship tonnage, being 5:5:3 for Britain, America and Japan. The Japanese had been pushing for a 10:10:7 ratio, but the Americans - having broken the codes in use between Tokyo and the Japanese delegation - were aware that the Japanese wouldn't hold out for this 10:10:7 ratio. So a 5:5:3 ratio was pushed and the Japanese "relented".

The trick was that this 5:5:3 ratio was actually beneficial to Japan, because they recognised that they couldn't beat America in a ship building contest. This would ensure that the gap between the Japanese and American navies would remain managable for the Japanese. But, because the 5:5:3 was seen as the Americans and the British getting what they wanted, Japan was able to receive guarantees that Britain and America would retain the status quo regarding naval bases in the Pacific. This basically meant that Japan didn't have to worry about new first-class naval bases in areas such as the Philippines or Hong Kong.

This isn't the whole story, but that's basically the gist of it.

Ian Toll has an excellent series of books on The War in the Pacific, and the first one (Pacific Crucible) briefly touches on this. Short answer: everyone wanted a naval treaty in the first place because they thought it would avoid war, and the naval treaty became a reality because (to oversimplify) everyone got what they wanted out of the Naval Treaty.

Slightly longer answer: the Europeans all saw the naval arms race between Britain in Germany as one of the principal causes of WWI and were keen to avoid another war. They were also all keen to reduce military expenditures after the expense of WWI, so the Naval Treaty was a bit of a "two birds, one stone" situation where the doves wanted it as a means of avoiding war and the hawks wanted it as a means of making military budgets go further.

And, as Geeism explained, the weaker powers agreed to the limits because they saw it as placing them on a more equal footing in naval terms than they otherwise would have been, while the stronger powers saw it as a means of securing their naval dominance without committing them to an unlimited naval building program (i.e. the British and Americans would continue to be the world's biggest naval powers without needing to construct endless numbers of expensive ships).

Both France and Italy were signatories to the Washington Naval Treaty of '21 (signed in Feb 1922). Everybody knows about the 5:5:3 ratio for the US, UK and Japan, but both France and Italy were assigned 1.75 limits. Further, both countries were limited to 60000 tons maximum of aircraft carriers (Japan: 81000, US and UK: 135000).

The Netherlands were not signatories to the Treaty.

An excellent, if somewhat dry, book on the topic is Warships after Washington: The Development of Five Major Fleets 1922–1930 by John Jordan.