Many, but the US Buster-Jangle Uncle effects test was the first. It was 1.2KTons exploded at a depth of about 3 feet, to test cratering effects. It produced massive fallout levels. Most underground testing is done much deeper to prevent contamination.
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All countries that have exploded nuclear devices have exploded their first devices. The USA was the first to detonate such a device and the only country to use nuclear warheads in combat. The most recent countries to test nuclear devices are India, Pakistan, and North Korea.
Both the first fission bomb (the Gadget device exploded in Trinity test July 16, 1945 on a 100 foot tall steel tower in the Jornada del Muerto valley in what is now White Sands Missile Range) and the first fusion bomb (the Sausage device exploded in Ivy Mike test November 1, 1952 on the surface at Enewetak Atoll) were designed and made at Los Alamos in New Mexico.
The use of a nuclear weapon on a country would be considered devestating, dependant on the payload and method of delivery of the nuclear device. It can destroy cities, and make the land infertile for many years afterwards please look towards Nagasaki and Hiroshima for more information. The "effect" of nuclear weapons on a country would depend on what your perspective is: there is something called MAD (Mutually Assured Destruction) of which the cold war is an example, where the development of a nuclear arsenal by one country (USSR) was profilgate in the development of a nuclear arsenal in another country (USA) this happened in many countries. Currently the body which is responsible for monitoring nuclear arsenals is called the IAEA (Internationl Atomic Energy Agency)
The only actions of consequence would be the 2 Atomic Bombs dropped on Hiroshima and Nagasaki in 1945. The USA are also the only country ever to use a Nuclear device against an Enemy country.
A small nuclear trigger (the primary) inside the weapon is exploded and used to generate energy, which is used to compress another device (the secondary) inside the weapon. This energy causes the secondary to collapse on itself, initiating a fusion reaction in the fusion fuel (Lithium6 Deuteride) contained in the secondary.