Messianic exegesis: There is long established tradition of seeing this passage as a Messianic prophecy. It is spoken by the mouth of a prophet to a worldly king after deriding that king's earthly context. Thus a Messianic prophecy establishing the true king might be seen as a appropriate response to Ahaz. Certainly it is difficult for many to read the passage and not evoke Handel's glorious musical paean to the Messiah.
The Messianic interpretation hinges on two pieces. the "virgin" and the name "Immanuel." The name would be considered a description rather than a name. and clearly the mortal Messiah was named Jesus (Yeshua). The name "Immanuel" means "God with us" which becomes an excellent description of the mortal Christ, though perhaps a stronger image for those who see Jesus and his Father as the same, and therefore Jesus as the literal embodied presence of God.
The appellation "virgin" is also very clearly related to the story of Mary. However, the selection of that term may also be dependent upon the Christian text, as the Hebrew almah might more properly read "young woman." Certainly a "young woman" might carry the connotation of "virgin," but the emphasis on her sexual status is explicit in the term "virgin" but not required in the concept of a "young woman." The term is clearly not the bethulah that has a much stronger connotation of "virgin," as would be expected in the text in Genesis:
Gen. 24:16
16 And the damsel was very fair to look upon, a virgin [bethulah], neither had any man known her: and she went down to the well, and filled her pitcher, and came up.
In other words, the current interpretation may be colored by our search for Messianic texts.
Contextual exegesis: In the context of Isaiah's prophecy, a purely Messianic interpretation of this text is impossible (though a dual prophetic intent can remain). The prophecy is given to Ahaz as a sign. It certainly is a poor sign for Ahaz if the fulfillment of the sign comes 700 years after his death. To be what Isaiah announced it to be, the sign would have to be something that Ahaz would be able to see fulfilled, and therefore be able to consent to the power of the Lord as seen through the sign given.
The nature of the more historical sign is understood better as the specifics of the sign are declared in the following verses.