The first thing you should know about the Battle of Bennington is that it didn't take place at Bennington in Vermont but rather it was fought near Walloomsac, New York, about 10 miles northwest of Bennington.
In mid-August 1777, after the fall of Ticonderoga, General Burgoyne planned a raid on the American stores at Bennington. His purpose was four-fold: to encourage the Loyalists, frighten New England, replenish his stock of provisions and to obtain horses to mount a regiment of heavily equipped German dragoons.* Accordingly, these dragoons, lumbering along on foot in their enormous jackboots and stiff leather breeches, were made the nucleus of a raiding force of about 800 Tories, Canadians, Indians, and English under the command of German Colonel Frederich Baum. Nearing Bennington, Baum learned that the American General John Stark had assembled about 1,500 troops at Bennington to oppose him, and he sent to Burgoyne for reinforcements. Colonel Heinrich von Breyman, with about 500 men, was sent to his aid.
In the meantime, Stark, hearing of Baum's advance, marched to meet him. His attack on the afternoon of August 16 exposed severe weakness in the English lines: Baum's command was too widely dispersed; his auxiliaries were scattered; and his regulars, hastily entrenched on a hill overlooking the Walloomsac River, were surrounded and most of them captured. Meanwhile, Breyman, ignorant of the battle, approached. Stark, now reinforced by Colonel Seth Warner with 350 men, re-formed and attacked. The Germans retreated and were pursued until dark. The Americans took about 700 prisoners. The victory did much to improve the morale of the American forces. (From US History Encyclopedia).
* Dragoons are soldiers intended primarily to fight on foot but trained also in horseback riding and cavalry combat.
The question is: How and where was Private Asa Pratt involved in all of this? The first task is to figure out what outfit Asa was serving with. I find in my genealogical notes from library research back in the 80's that Asa Pratt, private, was listed on the payroll of Captain Salmon Stone's Company in Colonel Nichol's Regiment of General Stark's Brigade "...raised out of the of the 15th Regiment of New Hmpshire Militia...which Company marched in July 1777 and joined the Northern Continental Army at Bennington and Stillwater." So thanks to a lot of hours digging through the sometimes dusty stacks of the Library of Michigan I know with whom Asa fought when he first was involved in actual combat.
About the General and the Brigade: "John Stark was one of those wild, untamed creatures like Ethan Allen (of Green Mountain Boys fame). Like a great many other outlaws in spirit, he had an intense passion for his native soil. New Hampshire was his domain. He was the uncrowned King of New Hampshire. He never actually joined the patriot army and refused to admit Congress had any jurisdiction over him. His troops were never part of the Continental Army but were an independent division of the New Hampshire Militia, who insisted that they were merely cooperating with he forces under Washington and were their own bosses." (from "Revolution 1776" by John Hyde Preston-1933)
Now that we know that Asa was with Colonel Nichols let's follow him into battle. Colonel Baum's troops are entrenched on a hill overlooking the Walloomsac River to the east.
"On August 16, the sun came out, the clouds broke away, and both sides prepared for battle...General Stark had pepared a rather complicated plan. A column of 200 men under Colonel Nichols (including Asa) was to make a long, flanking movement around to the north while another 300 men commanded by Colonel Herrick made a similar march around to the south. An additional 300 men led by Colonels Hobart and Stickney were to attack the nearest positions east of the river. When the flanking columns began their attack General Stark was to launch the main assault with 1,200 men directly across the river toward the center of the enemy's position".