OK, so we're talking about the Western Allies, not the Soviets here, right - which means France, Belgium, Holland and Luxembourg.

France was a bit of an odd case and I'm not an expert in wartime French politics, but:

1. The armistice of 1940 saw the Germans occupy the north and west of France, leaving the east and south to a pliant but technically independent government which moved to the spa town of Vichy.
2. Under international law, this Vichy government, headed by WW1 hero Marshal Petain, was the legitimate successor to the goverment that fell in 1940.
3. Vichy didn't declare war on the UK or US, nor did it join the Axis. It maintained its own armed forces and defended itself against attacks either against France or those colonies which remained loyal.
4. Meanwhile over in Britain, Colonel de Gaulle promoted himself to General and proclaimed a "Free French" government to continue fighting. Many French joined his forces, but several thousand of those evacuated from Dunkirk instead preferred to be repatriated to occupied or Vichy France and just go home.
5. de Gaulle spends the next four years in London being a right pain in Churchill's neck, always demanding the British invade this or that French colony held by Vichy.
6. Eventually, in 1943, US and British forces invade French North Africa in Operation Torch and in response the Germans occupy the rest of France and depose Petain. de Gaulle now has a more legitimate claim to represent the French government, but it's still a bit fuzzy.
7. Come the invasion of France, the Resistance mount a nationwide uprising and form a sort of militia, the Forces Francaises de l'Interieure (FFI).
8. Roosevelt is always suspicious of de Gaulle, suspecting he is using British and American troops to install himself as French president, and FDR initially orders US troops to bypass Paris and concentrate on pursuing the by now broken and fleeing Germans.
9. However, the FFI and Paris Police stage an uprising against the Germans as the allies approach and General Leclerc in charge of the Free French 2nd Armoured requests and eventually receives permission to go in and take the city.
10. As soon as he does, de Gaulle flies in and takes charge, installs himself as President and his officers as the new French government and sets about establishing control over France.
11. By the end of the war, around 10 months after the fall of Paris, the French armed forces have re-organised into independent units, the government is more-or-less functional and de Gaulle manages to have France recognised as one of the major allies at the post-war peace talks and to get a chunk of Germany to administer.

So, given that we're talking about four countries, one of which had a particularly odd situation, it's difficult to generalise, however:

Firstly, I wanted to ask what the procedure was following the >"liberation" of a nation. Using France as an example, assuming the >Germans were pushed out of the majority of France. Were there >internal hunter squads finding Germans in hiding? Did the Liberation >forces set up a garrison across the country to maintain it until wars >end?

Mostly, it wasn't needed; the Germans bugged out of France and Belgium pretty quickly all told and, aside from some nuisance sniping and booby traps there weren't any organised holdouts.

Civilian institutions like police and militia had been allowed by the Germans to remain in existence (albeit disarmed and under strict supervision) in all occupied territories, to provide security and to maintain the image of normality for the people. So when the Germans left, they simply kept doing what they were doing for the new bosses.

The biggest problem the liberating armies faced was that of collaboration and revenge - people who had been actively collaborating with the Germans were treated pretty brutally by their neighbours, and none more so than women who had been involved with German soldiers, either romantically or as prostitutes. They were usually dragged to the town square, had their heads shaved and various other humiliations heaped on them, were beaten up and forced to parade around with signs proclaiming their "sins".

Of course, the difficulty was that not every "collaborator" denounced was a genuine one; there was a lot of petty revenge and witch-hunts going around.

If you've a reasonably strong stomach, I can recommend the film "Black Book" (Zwartboek) as a very good depiction of these days in Holland.

What was the procedure for the nation re-joining the war following >liberation? Another example I'll use is France, but we all know about >the story of the Free French fighting alongside Britain and her Allies. >When the country was liberated, did their main army mobilize to join >the Allied effort or did they leave them to it? What about other >liberated European countries?

Again, France was the odd one out in that, determined to have a say at the end of the war, de Gaulle and the French government busted a gut to get re-armed and get troops fighting in their own formations as soon as possible to earn that place at the negotiating table. The Belgians and Dutch didn't so much - they were much smaller to start with, and hadn't been allowed to keep their armed forces like France. Those Belgians and Dutch already in the Allied armies stayed with their units, and I dare say more joined up, but those units remained part of the British Army rather than splitting off and forming their own.

What were the main problems faced by nations that were liberated >during the war, following the action? This extends, obviously, beyond >1945, but were there any major administration or social difficulties >involved with the Germans being driven out and control given back to >the nation?

Aside from the issue of collaborators and revenge mentioned above, the effects were profound on all levels - certainly economically, the Germans had taken many able-bodied men as slave labour and converted factories for war use, which had in turn been bombed by the RAF and USAAF to hurt the German war machine. In fact the British and US air forces probably did more damage to France than the Germans did in many ways. The Renault car factory, for instance, was re-tooled to make Panzers, then the RAF bombed it, then the Germans wrecked what was left before they pulled out. In 1945, Renault had a bunch of wrecked machinery, no workers and a handful of half-built tanks.

Socially, a lot of the most organised resistance movements had been Communist-oriented (particularly in France) and, with the Soviet influences in Eastern Europe there was a genuine fear that the economic wreckage of Europe would breed Communism in France and elsewhere. This was the reason behind the Marshall Plan - massive financial aid to all of Europe, any country that wanted it, including the former enemies, Germany and Italy and including the Eastern countries under Soviet domination. Not just financial aid, but shipments of stuff - coal, iron, wheat, tractors, cars, machine tools - whatever was needed to get the country moving again and forestall a communist revolution. Stalin forbid "his" bloc from accepting Marshall aid, of course.