Why and how were east Brandenburg, Pomerania and Silesia taken away from Germany after WW2?

Poland was simply ethnically cleansed by the Russians who force marched entire German families out of Silesia into east Germany.

Before there was any civil authority created in Silesia Polish Jews freed from incarceration created their own Freedom committees. For at least the first six months after Germany's capitulation these were the only real authority. These former Kz inmates took over whatever accommodations they wanted.

Addition to the answers given so far:

Since the Potsdam treaty (and other agreements between the "Big 3") was not signed by Germany itself, it was not a "real" peace treaty by international law. In fact, it does not declare that the mentioned territories are to be annexed by Poland .. merely occupied until a final peace treaty is signed (with the intention to weaken Germany and create a buffer zone to the Soviet Union, as said in other answers). This probably eased the acceptance of the treaty by the western Allies.

But the issue got a lot more complicated by the fact that two independent German states were founded after the war, one an ally of Poland, and one an enemy. Both sides denied the other the authority to sign a final treaty, delaying this step until 1990, when a reunited Germany could finally close the case once and for all.

Of course, by that time, the territories had been mainly inhabited by Poles for decades (and many former German inhabitants had died), and it was entirely unrealistic that they would be given back. But up until that point, the former German inhabitants of said areas had a reason to claim that they were de jure still German (this point of view was officially supported by the Western German government until 1970). If the Allies had signed a peace treaty with some strawman German representatives straight away in the late fourties, the whole issue would have had much less publicity. But the start of the Cold War got in their way.

You're right to say that Germany's loss of territory to Poland in 1945 was "harsh" judged by the principle that borders should be delineated according to ethnic and/or historical claims. No one then or since has tried to argue that the areas in question had been anything other than ethnically German for centuries

However Germany in 1945 was not any normal defeated power. It was allowed no voice in the settlement of its borders. Its utter defeat and devastation was of course one reason why it could not contest the settlement. For a long time after May 1945 there simply wasn't a state of Germany either practically or legally. This was one reason why the allied powers dismissed and arrested the Flensburg government (the government which continued to function - after a fashion - after Hitler's death). It emphasised that German statehood was now null and void.

Furthermore, German state or no German state, the victorious powers could justify transferring to Polish control large areas of formerly German territory:

1) Germany was perceived to need weakening so as to limit its capacity to once again renew itself after a defeat and wage aggressive war. In fact still harsher plans had been considered (e.g. the Morganthau plan).

2) The nazi policy of aggressive expansion and the crimes committed against Polish and Soviet civilians eliminated any squeamishness anyone might have had about expelling westwards large German populations.

3) In any case, as the other answer notes, a significant proportion of the local German population had already fled westwards even prior to fixing new borders

4) The idea of "shifting" borders west (the USSR expanding into Poland, Poland being compensated with parts of Germany), in order to create a sizeable safety buffer between the Russian heartland and Germany, was seen as reasonable in the light of Germany's two recent invasions of Russia (1914 and 1941).

You ask which treaties have defined Germany's loss of these territories. Wikipedia's German-Polish 1990 treaty article lists the key ones:

1945: Potsdam agreement
1950: Treaty of Zgorzelec between the DDR and Poland
1970: Treaty of Warsaw
1990: German-Polish Border Treaty

Borders

Post-war Polish borders were agreed upon in Teheran (1943) and finalized in Yalta (1945) by the "Big 3".

The land was taken from Germany on the grounds of Germany having started the war, to weaken it so that it would never be able to do that again.

Population

The Poles did not do the ethnic cleansing of those lands singlehandedly - at first the Germans ran away themselves, spurred by Goebbels's wildly exaggerated reports of the Red Army's atrocities (the atrocities were real, but the reports were exaggerated; in fact, there are some indications that the Red Army behaved differently in the areas which were to be given to Poland and Russia than in the areas which were to remain German).

Also, don't forget that Poles were also resettled.

Conclusion

I think one has to look at this episode in context: a horrible war just ended and the leaders set to the task of resolving the tensions which led to the war. The major source of tensions was people of one nationality living on the territory controlled by another (e.g., Germans in Sudetenland). So, to prevent those issues from re-appearing, massive population exchanges were undertaken, to ensure countries' ethnic h*m*geneity.

While many people suffered in the process, it was still done nicer than the similar attempt by the Germans during the war, and it did ensure that a similar conflict is now highly unlikely.