There are a few reasons why Napoleon could only muster around 75,000 men at Austerlitz. First, the Grand Armee had been fighting in the Ulm Campaign starting in October of 1805. Though it was a decisive victory for the French, battle casualties amounted to around 2,000. Not a huge number for an army of 230,000, but it fails to take into account other forms of attrition. Following the Ulm Campaign, the French took a number of casualties in two battles in November. They lost an estimated 4,000-5,000 at the Battle of Dürenstein and another 1,000 at the Battle of Schöngrabern.

Next, the French success during Ulm has been attributed to the strategy of la manoeuvre sur les derrières. Essentially, the French used their flexible corps to create a very broad front(As much as 100 mi during Ulm) while maneuvering other units into a flanking or enveloping position. Therefore, the Grand Armee was not always concentrated on one particular battlefield.

The entire Grand Armee at this time was comprised of seven Corps, the Imperial Guard, and the Cavalry Reserve. Lets look at the French Order of Battle for Austerlitz. The French had the I, III(a very small Corps at 4,000), IV, V Corps, Imperial Guard, a Grenadier Division, and Cavalry Reserve. They are missing 3 Corps, which was decent chunk of the army. It seems very reasonable that Napoleon could only had around 75,000 troops at Austerlitz.

Just to clarify, in 1805, the French army had about 400,000 men -the peak effective force during the Revolutionary period was about 700,000 men, but that leveled off relatively quickly to 400,000. Napoleon trained about 200,000 men to be the Army of England, but when they were deployed to Central Europe, they became the Grande Armee, originally in seven numbered corps (later eight).

At Austerlitz, Napoleon had I Corps, III Corps, V Corps, IV Corps, the Guard, and Murat's Cavalry Reserve, for a total of 75,000 men. Not present at the Battle of Austerlitz were VIII Corps, which was south of the Danube, II Corps, which was observing the Archduke Charles's army of Italy north of Graz in the Tyrol, VI Corps, around the Salzach river, and VII Corps, in the Ulm area. So as many corps as Napoleon had in the bulk of his army were strung out across southern Germany, and they had taken casualties during the Ulm campaign and the subsequent pursuit engagements along the Danube. von Clausewitz listed the act of marching as one of the forces that actively destroys an army, and the Grade Armee had marched well over five hundred miles as the wolf runs since the commencement of the campaign in late September. The temperature was dropping through October and November, with the climactic battle taking place in early December. Racing down the Danube, the men were physically exhausted by the cold and the long marches, living in unsanitary conditions, and billeted with a foreign population, they encountered local strains of diseases their immune systems couldn't effectively combat.

There were furthermore four large depots stretching from Vienna back to Strassburg, as well as smaller garrisons throughout the occupied territory along the Danube. The main Austrian army was in the Italian theatre, and there was a danger that it would use the passes through the Alps to attack the Grande Armee's long line of communications back to France.

Between combat losses, the need to establish lines of communication and depots and observe enemy forces, and wastage arising from disease, exhaustion, and desertion, the fact that Napoleon could still muster what would have been an exceptionally large field army by 18th century standards hundreds of miles through occupied territory from its base areas is remarkable to say the least.

Others have already given answers regarding more specific details, so I'll speak more in the abstract of military strategy. Armies in this period faced immense logistical challenges when on campaign, not least because the concept of levee en masse was relatively new. However, armies on the offensive in particular face unique difficulties which they must remedy as best they can.

In my view, chief among these difficulties would be a hostile populace. Typically speaking, the people of the country you are invading (or even just marching through on your way to invade somebody else) won't like you very much - at best you're disrupting trade that could be their lifeblood in terms of income, food, etc. - at worse you're stealing precious goods and horses, taking or even destroying livestock and crops, brutalizing their friends, family, and loved ones, setting their cities ablaze, and shooting at their brothers, fathers, and sons who are in uniform defending the land from you as you do so!

There are many difficulties which arise for an invading army from having to deal with hostile locals. Not only does such a scenario totally eliminate the possibility of local collaborators informing you of enemy troop movements, but they report your movements to the enemy as well as potentially riot or form guerrilla bands to harass your supply and communication lines (as they did in Spain). This in turn leaves your army blind and your supply and communication lines vulnerable, meaning you need to detach forces to guard your flanks along the entire route of the march - after all, you can't see the enemy, you don't know if they're planning to cut you off or not. Better to have a flank guard and not need it, than need it and not have it.

In addition, as mentioned above, hostile civilian forces may attempt to report movements to the enemy - but only the ones they can see without having to move from home. Keep in mind that this is still in the timeframe when most people didn't stray more than 20-30 miles from their place of birth unless they were in the army or otherwise had the resources to do so (which most didn't), and the human eye can only see so far from an on-the-ground elevation. Armies in this period often deployed what is known as a screening force, detached from the main body of an army and placed between it and the enemy, to conceal the main body's movement. This would protect the army's supply and communication lines from harassment, allowing the main body to go on at full speed, unscathed.

This means, however, that the army would need to deploy along a much wider front - perhaps the main body marching along one or two roads, a corps acting as a screen twenty to forty miles north on another road, another corps the same distance south on another road, a total frontage of forty to eighty miles, stretching over 400 miles (in the case of Austerlitz) from the French border to the interior of the Austrian empire - in order for the screening forces to be far enough away that the movements of the main body can't be observed by those who can see the screening forces (as it's unlikely that anyone inside the area occupied by the French army would be able to send word out of that area, there would be French patrols on the roads or something to that effect checking people's luggage).

Finally, when speaking of the movements of the main body, it's important to remember that much of war is also mind games. You never want to let the enemy know where the main body actually is. This means you need to leave enough troops out on each flank to distract the enemy and occupy their attention, enough troops to be a threat anywhere, while keeping your true intentions concealed. Often times this means more than half of your army can be partitioned out to keeping other fronts locked down, making commanders there worry about if that is where you want to strike, and thus keep forces there to guard against any potential move you make; all the while you move the largest single piece of your army moves in for the decisive conflict against the enemy who has, hopefully, weakened himself sufficiently from guarding against your feints that you can deliver a knockout blow. (Finding the enemy though - that's its own challenge.)

EDIT:

I decided to make an illustration of what I'm talking about so you and others can get a better mental picture of what I mean. (It's on Google Docs because my internet is too slow for Imgur right now. Darn holidays.) Please keep in mind this is most certainly NOT an illustration of the ACTUAL Austerlitz campaign, I haven't studied that, I'm merely trying to provide a reference for the concepts I'm explaining. I'll allow others to comment on specific examples of these principles being applied in real life history. But in general, the reason why so few troops were committed to field battles as compared to the size of armies taking part was because of the need to guard flanks, both to protect interior lines of supply and communication as well as to conceal your true intent as you prepare to deliver a knockout blow to the enemy.

An especially important factor is the need to deploy troops for contingencies. This includes garrisons and troops deployed to deter or guard against potential enemy attacks. In particular, during the Hundred Days, Napoleon raised an army of nearly 250,000 active troops, but these were distributed among multiple areas. Marshal Suchet and General Rapp each had about 23,000 men, the former guarding the Alps and the latter posted to the Rhine. Two (rather undersized) corps were sent to the Pyrenees, and a third to the border with Piedmont-Sardinia, totalling 20,000 men. 20,000 were sent to the northwest, and another 20,000 remained in Paris. In other words, over 110,000 of 250,000 men were not in the main army in Belgium. I don't have my copy of David G. Chandler's The Campaigns of Napoleon immediately accessible for more exact figures, but this map illustrates the situation serviceably.

In addition, for the French, the war was multi-fronted, as, aside from the German, Italian, Polish and Russian campaigns, they had to deal with the Peninsular War. At Bailén in 1805, the surrender of a whole army corps halved the size of the French army in Spain, and by the end of the year, the French had 80,000 men in the Peninsula. Over the course of 1808-1814, over 250,000 French soldiers had been deployed to the Iberian Peninsula (albeit not all at once).

To some extent, armies could not afford to be particularly large. Napoleonic armies often thrived on foraging rather than fixed supply lines, attested from the propensity of French soldiers to loot the countryside. One contemporary expressed shock that he saw a chicken in the camp of Marshal Davout, as, had it been the camp of any other corps (Davout was an infamously strict disciplinarian) it would have been killed an eaten on sight. This would be disastrous in 1812, when Napoleon's troops could not forage, but had virtually no supply wagons to assist. Of 600,000 invaders, only 110,000 returned (most of them deserters – Napoleon crossed the Berezina into Poland with only 27,000 at the end of the campaign). If one chose not to pursue an unrestricted supply gathering policy, one would have a significantly smaller army to command. The British Army, for example, paid locals for supplies and shelter, and the Anglo-Portuguese field force never rose above about 80,000, and often fought with roughly even numbers to the French.