What do those who dispute extermination say happened?

They say that what actually happened was what the Germans said was happening. "Evacuation to the East" was not code but actual policy. The "showers" were not gas chambers but showers, and Zyklon B was used for its proper purpose, killing lice.

Before the war
Here there is no disagreement with orthodox history. Nazi policy was to drive the Jews out of Germany by a combination of stick and carrot. (Germany was not alone in this. Poland also discriminated against and sought to expel its minority communities, including both Jews and Germans.) This led to economic reprisals by international Jewish bodies, which in turn hardened Nazi attitudes even further. Jews were deprived of German citizenship but allowed to have their Jewish organisations and fly the Star of David flag. Jewish nationalism and separatism were encouraged. Emigration was encouraged and assisted. Jews were allowed to transfer a substantial proportion of their assets abroad. Western countries were for the most part unwilling to accept these emigrants. Zionist organisations cooperated with the German authorities in the Haavara agreement to promote emigration to Palestine. By 1940 two thirds or more of Germany's 600,000 Jews had left Germany. Poland followed a similar anti-Jewish policy and cooperated with Germany, but this is inconvenient to the narrative of unique German evil so it is generally passed over in silence these days. As Poland's Jewish population was much greater, the proportional reduction was much less and the Germans found a large Polish Jewish population when they invaded. Whereas the German Jewish population had been for the most part integrated, educated, affluent and German-speaking, Polish Jews were less affluent and tended to live in their own Yiddish-speaking communities.

Outbreak of war
Still no disagreement with orthodox history. Polish Jews were viewed as a security risk and confined to ghettos and employed in the war effort. The ghettos were policed by Jewish collaborators who cooperated in supplying Jewish labour. Labour camps and concentration camps were established, the largest being Auschwitz, a massive complex which supplied labour to the IG Farben chemical works.
After the Fall of France, the plan to set up a Jewish homeland in Madagascar (first floated in 1937 by Poland!) was revived, but had to be abandoned as impractical since Britain controlled the sea routes.

War with the Soviet Union
It was decided that the "Final Solution" of expelling Jews from Europe would have to wait and that Jews would be sent East to territories evacuated by the Soviets. Those who could work would be employed in the war effort.
Here the disagreements with orthodox history begin. Small transit camps were set up at Treblinka, Sobibor and Belzec, on the border between the General Gouvernement (Polish territory occupied by Germany in 1939) and the captured Soviet zone of Poland, where deportees went through a delousing process. Typhus was endemic in Eastern Europe and always flared up at times of disruption and war: it was typhus that destroyed Napoleon's army in 1812. It is spread in the faeces of lice and penetrates the skin when people scratch themselves. Hygienic precautions included showering to wash away the faeces, head-shaving to remove lice and nits, and delousing clothing with hot air, steam or cyanide gas (Zyklon B). Orthodox history claims that these delousing stations were in fact murder camps with gas chambers using diesel exhaust, which in reality is not toxic. (There is some ambiguity about Sobibor, which is sometimes said to have used petrol-engine exhaust. Zyklon B gassing is not alleged for these camps, only for Auschwitz and Majdanek)
At Auschwitz there was a massive outbreak of typhus in 1941. The existing cremation facilities, designed to cope with a normal death rate, were overwhelmed and some open air incineration of bodies took place. More extensive cremation facilities were set up to be able to handle any future outbreaks. Next to each crematory was a morgue. These morgues are alleged by orthodoxy to have been used as gas chambers for mass murder.

What happened to the Jews of Europe?
Estimating population numbers before, during and after the Second World War is fraught with difficulties. There is no agreement on pre-war or post-war Jewish populations and emigration, or on the number of Jews actually under German control during the war. Revisionists claim this number was well under the iconic 6 million. They generally place actual losses somewhere around a million, but accept as possible the very wide range of as low as 500 thousand to as high as 3 million.
  • An unknown number died in camps, in regular armies, as partisans and as civilian victims of war, including reprisals and bombing.
  • Jews were likely to be singled out in reprisals because of official and personal attitudes to Jews, and because they were predominant among partisans and Communist party commissars.
  • The conditions of the evacuation to the east under wartime conditions were harsh by the Germans' own admission, and can reasonably be presumed to have caused a substantial but unknown number of deaths
  • After the Soviet forces withdrew, there were anti-Jewish riots in the Baltic countries, where Jews were perceived to have collaborated with the Soviet occupiers who had deported and murdered many local people, and in Ukraine where they were held responsible for the 1930s famine caused by forced collectivisation.
  • Further unknown numbers fled to Soviet-occupied Poland in 1939 and Jews from here and other areas occupied by Germany in 1941 fled or were evacuated by the Russians, many of them to the Urals and Siberia where housing was insufficient and inadequate and many can be expected to have died. Others died in the general conditions of war. Some survived in the Soviet Union and some managed to escape and emigrate to Western countries when the war ended.
  • The Hungarian Jews allegedly gassed at Auschwitz in 1944 were actually sent to camps in Germany and Poland. Many subsequently died in transit or in the camps.
  • Many died in the westward evacuation of the Eastern camps and in the awful conditions in the Western camps at the end of the war, but they were not gassed or otherwise deliberately killed.
  • After the war many more Jews than is generally realised remained in Poland and Hungary. They actually ran the Communist regimes there in the immediate post-war period. (This is verifiable.)
  • Many Jews, especially Communist atheist Jews, simply assimilated taking Polish, Russian or other names.
  • Jews unable or unwilling to return to their former homes in Eastern Europe emigrated all over the world, many finishing up in Israel and the USA, as well as Britain, France, Australia, South Africa and South America. These also frequently changed their names, making tracing them difficult, so that relatives would believe them to be dead.
  • The largest group of Western Jews, the French, was largely untouched. Most of the deportations from France concerned recent immigrants from Central and Eastern Europe and persons (Jews and non-Jews) arrested for Resistance or black-market activity. Prominent French Jews such as Henri Krasucki and Simone Veil did return from captivity in Auschwitz. The Dutch were the only large group of Western Jews to be deported systematically.
Only one Revisionist and one orthodox demographic study have been undertaken. The Revisionist study(1) by Walter Sanning (an American University professor) estimates a total of 2 million Jewish deaths from all causes, of which 300 thousand can be attributed to German actions. The orthodox study(2), which was undertaken to counter Sanning, finds, unsurprisingly, 6 million dead. The main difference between the two is that Sanning finds many more evacuated to the Soviet Union (including Siberian labour camps), and higher numbers of surviving emigrants.

(1) Sanning, Walter. The Dissolution of European Jewry
(2) Benz, Wolfgang. Dimension des Völkermords