This answer is only semi-relevant, but Sun Tzu offers some tips for scouts.

Movement amongst the trees of a forest shows that the enemy is advancing. The appearance of a number of screens in the midst of thick grass means the enemy wants to make us suspicious.

The rising of birds in their flight is a sign of an ambuscade. Startled beasts indicate that a sudden attack is coming.

When there is dust rising in a high column, it is the sign of chariots advancing; when the dust is low, but spread over a wide area, it betokens the approach of infantry. When it branches out in different directions, it shows that parties have been sent to collect firewood. A few clouds of dust moving to and fro signify that the enemy is encamping.

and

When some are seen advancing and some retreating, it is a lure.

When the soldiers stand leaning on their spears, they are faint from want of food.

If those who are sent to drink water begin by drinking themselves, the army is suffering from thirst.

If the enemy sees an advantage to be gained and makes no effort to secure it, the soldiers are exhausted.

If birds gather on any spot, it is unoccupied. Clamour by night betokens nervousness.

If there is a disturbance in the camp, the general's authority is weak. If the banners and flags are shifted about, sedition is afoot. If the officers are angry, it means that the men are weary.

When an army feeds its horses with grain and kills its cattle for food, and when the men do not hang their cooking pots over the camp-fires, showing us that they will not return to their tents, you may know that they are determined to fight to the death.

As for the number of soldiers, I assume they would make a rough estimate. If they had time, they would count the number of tents.

Many scouts would simply attempt to "eyeball" the number of enemy soldiers if there was no other reliable means for determining their number, often with drastically incorrect results. Other than that, it was common for enemies to attempt to estimate the strength of a foe by counting the banners of his army, especially when faced with a disciplined force. If, for example, you had some knowledge of Roman formations, you might know that each century had either 100 or 80 men, depending on the year. From that you could try to pick out individual centuries and estimate the number of soldiers. It was exactly this type of scouting which led the Byzantines to drastically vary the number of men in each of their formations, so as to confound attempts to use organizational banners to estimate their strength. I'm not sure what other methods were used to estimate the strength of less organized forces, other than observing their camps.

In Medieval Japan, it was possible for a trained scout i.e. ninja to estimate the size of an army by counting the flags. Many samurai, which formed the cavalry in Japan, carried flags to help distinguish themselves on the battlefield. Ashigaru infantry and archer or arquebuse formations also had flags to denote them. By counting the number and type of flags, one could calculate the rough number of troops in an army, as well as the individual commanders and generals who were present.