Expanded from an earlier answer of mine

In terms of notice, FDR signed Executive Order 9066 in 19 February 1942 which authorized exclusion of enemy aliens in what were termed "Military Areas", on 2 March Lieutenant General John L. DeWitt declared the Pacific Coast "Military Area No. 1", and throughout the rest of March a series of edicts restricts Japanese-American movement in Military Area No. 1 and control over their assets. Additionally, War Relocation Authority (WRA) starts opening up camps like Manzanar. By late March, internment began to assume a reality and by April 1942 the process is well under way. So in terms of notice, the timeframe is very brief (February-March 1942). It is also important to realize that from the perspective on the ground, it is difficult to disentangle these various initiatives from wider wartime security regulations (e.g. blackouts, curfews, etc.) and DeWitt's proclamations were often quite confusing. Military Area No. 1 was initially only 100 miles inland, leaving Military Area No. 2 (the inland West coast) nominally free from these restrictions, leading some Japanese-Americans to make plans to move there. But DeWitt's Public Proclamation No. 4 of 27 March forbid Japanese-Americans from Area No. 1 to move to No. 2, thus trapping many in Area No. 1.

The relative suddenness of internment is one of the reasons why it was so economically devastating for the Japanese-American community. Many Japanese-Americans were involved in farming and their farms were among the most productive in the West Coast. The Congressional Commission on Wartime Relocation and Internment of Civilians (CWIC) of 1980 estimated that of 6,118 farms valued at $72 million with $6 million worth of equipment. Most of these farms had to be sold at firesale prices and the result was a net loss for the West Coast agricultural economy in 1942 as the evacuations took place at peak spring harvest. Shop owners and other business-owners had to liquidate stock and stores quickly. Assets in Japanese-owned banks were frozen and home owners likewise had to sell their houses.

The Japanese-American community as a whole did not have that much access to ready cash as the Roosevelt administration had before Pearl Harbor had restricted the activities of Japanese-owned banks in the US, which a number of Japanese-Americans had accounts in as it was easier to send money back to the Home Islands. After Pearl Harbor, the ability of "enemy aliens" to withdraw money from their accounts was also frozen. Bank accounts in American banks remained in service, but their holders could not access them until the middle of the war when Eleanor Roosevelt appealed to the US government to allow internees access to their holdings, albeit still on a limited basis. The Federal Reserve Bank was charged with protecting the financial interests of the internees, but its portfolio also included the task of ensuring that evacuation be accomplished as swiftly as possible. These two imperatives were incompatible and most FRB personnel prioritized the latter imperative. Despite this, the FRB often assured Japanese-Americans that their property would be safe if they could not sell it. Not only were there too few FRB personnel to make this a reality, they often underestimated the complexity of evacuation process. For example, cars were a form of movable property that could not be off-loaded easily, so a number of internees simply drove their cars to the evacuation centers and left them there in the hopes of being able to return and claim them once resettlement had settled down. Eventually, this became such a problem that the FRB demanded that the evacuees sell their automobiles to the US Army at FRB-evaluated prices. This was something that repeated itself in multiple areas where property that could not be carried off or sold was often left in place in the hope that it could be reclaimed. Theft, arson, and vandalism were the natural end results of this policy and neither local authorities nor the federal ones were inclined to investigate or discourage such actions.

But the financial losses were not just in concrete assets like homes, farms, automobiles, and shops. Wartime relocation and internment also meant that for a good three years, a large segment of the Japanese-American population was simply out of the workforce. The WRA camps paid wages to internees for jobs performed on site such as cooking, but these jobs paid below average rates and many internees were reluctant to participate in a system that had hurt them in many ways. Being locked out of the wartime economy meant the Japanese-American community did not by and large receive its collateral benefits. Not only did the war economy improve workers' wages, but wartime industries provided job training and other skillsets, as well as social networks for the postwar period. Many Japanese-Americans found their skillsets atrophy in the camps. This posed problems for the postwar period of adjusting to the end of internment. The economist Aimee Chin compared interned male Japanese-Americans interned to Hawaiian Japanese, who were not interned en mass, and found that by comparison internees' annual earnings were 9-13% less than those who escaped internment. Internment also encouraged many Japanese-Americans to funnel their resources into so-called human capital such as education instead of physical investments like buildings or businesses.

The above makes it very difficult to put an exact price tag on the cost and losses of internment. The actions of the US government during the war and the immediate aftermath made this much harder. The 1948 Evacuation Claims Act allowed for some compensation, but the IRS had destroyed the tax records for 1939-42, making evaluating the claims near impossible. The suddenness of internment also meant that internees found it difficult to preserve financial records when they were allowed only a finite amount of personal property (as anyone who has moved knows, paper in bulk is quite heavy). Japanese-Americans claimed $148 million in losses in 1948, but the government only paid out $37 million. The oft-quoted figure of $400 million which came from the Federal Reserve Bank of San Francisco is one that is often cited, but this is one of those numbers like the million casualties for an invasion of Japan; there is no real data or even research to back up this figure. Broom and Riemer's 1949 book Removal and Return: The Socio-Economic Effects of the War on Japanese Americans provided a more conservative figure of $77 (1941 dollars) million in property losses. Broom and Riemer extrapolated data from Los Angeles property records and was one of the most thorough estimates produced of losses close to the time of evacuation. But Removal and Return's estimates are likely on the conservative end of things as they do not account for intangibles like loss of productivity and other aspects related to property loss.

Of course dollar value cannot really quantify other losses, such as the psychological trauma of internment and dislocation. George Takei's memoirs for example recall arriving back on the West Coast and only being to live in a slum and being immediately greeted by a bum urinating, a fact that frightened his younger sister. Such stories, as well as others about losing family heirlooms or seeing the hard work of decades washed away over the space of a few months, which are quite common among internee memoirs, speak to intense psychic costs of internment and add a further blot to this gross violation of Japanese-Americans' civil rights.

Sources

Chin, Aimee. "Long‐Run Labor Market Effects of Japanese American Internment during World War II on Working‐Age Male Internees." Journal of Labor Economics 23, no. 3 (2005): 491-525.

Ng, Wendy L. Japanese American Internment During World War II: A History and Reference Guide. Westport, Conn: Greenwood Press, 2002.

United States Commission on Wartime Relocation and Internment of Civilians. Personal Justice Denied. Wash., D.C.: Civil Liberties Public Education Fund, 1997.

Why did the IRS destroy tax records during this period?