StarLight: Herodotus quoted a figure of some 3 million Persian troops. This is generally regarded as a massive exaggeration. However it is known that the Persian army considerably outnumbered the Greeks. At that point the Greeks had a force of some 30,000 infantry. The actual size of the Persian army is not known but has been estimated at anything from 150,000 to 300,000 troops.
This figure may seem vast for the ancient world but there is plenty of evidence for it.
Note that about this time the various Chinese states were fielding armies in the hundreds of thousands. The Roman Empire fielded an army, which generally numbered approximately 400,000, but at its numerical peak reached as much as 600,000.
As for financing - well look at it this way. The Persian king is an autocrat in every sense of the word. If he says they're going to invade Greece with the biggest bloody army that part of the world had ever seen then that's whats going to happen. If the treasury hasn't enough then they'll just raise taxes & to hell with public opinion.
Also the Persian Empire spanned Southern Asia & commanded the Trans-Asian trade routes. That's a lot of money. When Alexander the Great overthrew the Persian Empire about 150 years later he ended up with a booty in excess of 180,000 talents of gold - in other words the Persian Achemenid Kings were the 5th & 4th century BC equivalent of Bill Gates.
Finally where did they get all the manpower? Simple - the Persians saved heaps on training & weapons production because they didn't have it. The quality of Persian troops varied from untrained conscripts to the elite 'Immortals' - perhaps the only really professional fighting unit in the whole army. Each unit supplied its own equipment - as attested to by the fact that the Greek observers could readily identify between the different nationalities. And the baulk of the army - levied conscripts, who received no formal training, were drafted from wherever.
The Greeks never had an army numbering 100,000 in those days. As for the final battle (the Battle of Plateau, 479 BC) the Persian King Xerxes I had withdrawn back to Asia Minor (Ancient Turkey) with the baulk of his army. After the actual battle many of the Persians would have escaped rather than be slaughtered.
