This conflict between a coalition of states including Israel and Syria against Judah is the political background to the first section of the Book of Isaiah (Is 7). It is described in the Books of Kings and Chronicles (2 Kg 16, 2 Chr 28).
Before this time, Tiglath-pileser III of Assyria, also known as Pul, started expanding his empire to the south-west. King Menahem of Israel had to pay tribute to him to persuade him to withdraw from Israel (2 Kg 15:19). Tiglath-pileser later returned during reign of Pekah and conquered all of northern Galilee (2 Kg 15:29).
While Ahaz reigned in the south (Judah), Pekah reigned in the north (Israel). Pekah was threatened by Assyria and formed a coalition with Syria, Askelon and Gaza against them (2 Chr 28:18). Ahaz was invited to join the coalition, but he refused, so the coalition, led by King Rezin of Syria decided to attack Judah.
Attacks began under the reign of Jotham (2 Kg 15:37). Israel and Syria attacked separately (2 Chr 28:5-6) and jointly (2 Kg 16:5). Ahaz was captured by Rezin and taken to Damascus and captives were taken to Samaria (2 Chr 28:5). Edom took advantage by attacking Judah at the same time (2 Kg 16:6).
Rezin and Pekah's plan was to usurp Ahaz and put the son of Tabeel as an anti-Assyrian puppet on the Davidic throne, thus destroying the Davidic line (Is 7:6). Ahaz was afraid: "When the house of David was told, "Syria is in league with Ephraim", his heart and the heart of his people shook as the trees of the forest shake before the wind". (Is 7:2).
As Ahaz was going to inspect the water supply, Isaiah met him with a prophetic word, "Take heed, be quiet, do not fear and do not let your heart be troubled because of these two smouldering stumps of firebrands, at the anger of Rezin and Syria, and the son of Remaliah (Pekah)" (Is 7:4). Ahaz was given the choice to trust in Assyria or to trust in God. The choice is not between being pro- or anti-Assyrian, but to be pro-God. Isaiah offered Ahaz the prophetic sign of his choosing (Is 7:9), to confirm that his word concerning Samaria and Rezin was true. He warned that the consequence of not trusting God and calling upon Assyria for protection would lead to invasion by Assyria (Is 8:5-8).
Ahaz refused God's offer to trust him and called on Assyria to assist him in defeating his enemies (2 Kg 16:7-9, 2 Chr 28:16). This contrasts with Hezekiah, who did trust God (Is 36-39).
Assyria gladly accepted Ahaz's request and invaded Syria and Israel. Firstly Galilee was captured by Assyria in 734 BC (2 Kg 15:29), then the tribes of Reuben, Gad & half-Manasseh were captured (1 Chr 5:26). Syria was taken and Rezin killed, 734 BC (2 Kg 16:9). Of the northern kingdom, Samaria alone was left, and held out until 722 BC. Pekah was assassinated, and Hoshea was placed as a puppet king on the throne of Samaria.
Ahaz's alliance backfired on him. Assyria turned around and invaded Judah, causing much damage (2 Chr 28:20-21, Is 7:17). Judah became a vassal of Assyria, had to pay tribute, and was forced to recognise the Assyrian gods (2 Kg 16:10-16, 2 Chr 28:20-21) which included building an altar like one in Damascus in the Jerusalem temple.