Right there in Isaiah. Let's go through this one step at a time.
1. To whom is the prophecy made? King Ahaz.
Again the LORD spoke to Ahaz, [11] "Ask a sign of the LORD your God; let it be deep as Sheol or high as heaven." (Isaiah 7:10-11)
2. What does the prophecy pertain to? The failure of the armies of Syria and Israel to defeat Judah.
In the days of Ahaz the son of Jotham, son of Uzzi'ah, king of Judah, Rezin the king of Syria and Pekah the son of Remali'ah the king of Israel came up to Jerusalem to wage war against it, but they could not conquer it...
[7] thus says the Lord GOD: It shall not stand, and it shall not come to pass. (Isaiah 7:1,7)
3. What was the purpose of the prophecy? To calm the fears and strengthen the resolve of Judah.
[2] When the house of David was told, "Syria is in league with E'phraim," his heart and the heart of his people shook as the trees of the forest shake before the wind.
[3] And the LORD said to Isaiah, "Go forth to meet Ahaz, you and She'ar-jash'ub your son, at the end of the conduit of the upper pool on the highway to the Fuller's Field,
[4] and say to him, `Take heed, be quiet, do not fear, and do not let your heart be faint because of these two smoldering stumps of firebrands, at the fierce anger of Rezin and Syria and the son of Remali'ah.
[5] Because Syria, with E'phraim and the son of Remali'ah, has devised evil against you, saying,
[6] "Let us go up against Judah and terrify it, and let us conquer it for ourselves, and set up the son of Ta'be-el as king in the midst of it," (Isaiah 7:2-6)
4. When would the prophecy be fulfilled? Very soon!
For before the child knows how to refuse the evil and choose the good, the land before whose two kings you are in dread will be deserted. (Isaiah 7:16)
So, Ahaz, King of Judah, fears the invaders. God sends Isaiah to reassure him that he will prevail. Ahaz is reluctant to ask for a sign, so God tells him that before a particular child, soon to be born of a woman apparently known to both Isaiah and Ahaz, is old enough to know the difference between good and evil, Judah will prevail in its war with Syria and the northern kingdom. Furthermore, this will usher in a period of peace and prosperity.
Now, when do we actually see this prophecy fulfilled?
And I went to the prophetess, and she conceived and bore a son...
Behold, I and the children whom the LORD has given me are signs and portents in Israel from the LORD of hosts (Isaiah 8:3,18)
All of these events--the birth of the child of the young woman, the war with Syria and the northern kingdom, and the final victory of Judah over its foes--took place within several years of Isaiah's prophecy. Thus, "before the child knows how to refuse the evil and choose the good", the prophecy had been fulfilled.