In Summary...

After this David defeated the Philistines and subdued them, and David took Metheg-ammah out of the hand of the Philistines. And he defeated Moab and he measured them with a line, making them lie down on the ground. Two lines he measured to be put to death, and one full line to be spared. And the Moabites became servants to David and brought tribute. David also defeated Hadadezer the son of Rehob, king of Zobah, as he went to restore his power at the river Euphrates. And David took from him 1,700 horsemen, and 20,000 foot soldiers. And David hamstrung all the chariot horses but left enough for 100 chariots. And when the Syrians of Damascus came to help Hadadezer king of Zobah, David struck down 22,000 men of the Syrians. Then David put garrisons in Aram of Damascus, and the Syrians became servants to David and brought tribute. And the LORD gave victory to David wherever he went. And David took the shields of gold that were carried by the servants of Hadadezer and brought them to Jerusalem. And from Betah and from Berothai, cities of Hadadezer, King David took very much bronze. When Toi king of Hamath heard that David had defeated the whole army of Hadadezer, Toi sent his son Joram to King David, to ask about his health and to bless him because he had fought against Hadadezer and defeated him, for Hadadezer had often been at war with Toi. And Joram brought with him articles of silver, of gold, and of bronze. These also King David dedicated to the LORD, together with the silver and gold that he dedicated from all the nations he subdued, from Edom, Moab, the Ammonites, the Philistines, Amalek, and from the spoil of Hadadezer the son of Rehob, king of Zobah. And David made a name for himself when he returned from striking down 18,000 Edomites in the Valley of Salt. Then he put garrisons in Edom; throughout all Edom he put garrisons, and all the Edomites became David's servants. And the LORD gave victory to David wherever he went. (2 Samuel 8:1-14 ESV)
In chronological order, these victories actually happened before chapter 7 - before David had rest from all these enemies of Israel. This is a summary of those enemies. Taking a map of the day, in short, these were enemies in every direction. David left the Philistines a little sliver by the Sea, the enemies to the South very little but desert, and pushed those to the East and West so far that their neighbors paid tribute to keep David away. But the true summary is in the last verse. The LORD gave the victories. It was Him, not the courage and cunning of David. David had a history of fear and some shaky alliances when he did not seek God's direction. But now David had victory after victory as God gave him courage and wisdom on where, when and how to fight his battles. That is the summary, the key, to victorious living.