Ancient Macedonian was either a northern Greek dialect or a language very closely related to Greek. Most Ancient Macedonian names and words that we know of are clearly of Greek origin, although there are also some known words that appear to come from Illyrian and Thracian, Indo-European languages of which we know very little. Unfortunately, we don't really have that many words that are explicitly identified as Ancient Macedonian. By Alexander's time, the upper classes spoke Attic Greek, the variety of Greek spoken in and around Athens which came to be a lingua franca of the Hellenic world and evolved into Koine. But the army grunts still spoke Macedonian among themselves:
Despite the importance of Attic and Koine Greek for official purposes in the kingdom, ancient Macedonian still was the common language among many ordinary Macedonians in the army in the late fourth century. This observation may be deduced from several passages about speeches and commands given to the Macedonian soldiers in the time of Alexander the Great and the early Diadochoi. First there is a hint in the patrius sermo (the Macedonian dialect) during the Philotas affair (Curt. 6.9.34– 36).42 Philotas is mocked in the Assembly of Macedonians for not speaking in Macedonian. Further, Plutarch reports that during the fatal drinking party that cost Cleitus his life Alexander shouted an order in Macedonian when he was summoning his guard with an emergency command while Greek was the usual language of command in his army (Alexander 51.4–6). Then in 321, when the Greek Eumenes defeated the forces of Neoptolemus, he successfully sent an Macedonian officer named Xennias to address the phalanx troops in Macedonian speech (PSI 12 1284, Plut., Eumenes 5.3) and in 317/16 the same Eumenes was greeted by his troops ‘in their Macedonian speech’ (Plut., Eumenes 14.5, 11); probably these were the ‘Silvershields’.
Source: A Companion to Ancient Macedonia, edited by Roisman and Worthington, chapter 5, "Macedonians and Greeks", by Johannes Engels.
Unfortunately any non-scholarly discussions of these kinds of things tend to be muddied by modern disputes between the peoples who inhabit that area today. So let's please not get into that.
Some good literary evidence on the issue - Livy wrote "Aetolians, Acarnanians, Macedonians, men speaking the same language.
Curtius stated that the Macedonians had "community of language" with the Brachindae.
Also from Currius, Philotas states that the Greeks will "understand better" if he speaks in Attic and not Macedonian. That would imply that Macedonian was intelligible to a degree for other Greek speakers.
Livy also recorded a Macedonian ambassador telling that the Aetolian Assembly that the Romans were "foreigners, separated from us by language" and that a Latin proclamation for the Romans was "translated into Greek" for a crowd of assembled Macedonians.
In terms of archeology, there's the Pella Curse Tablet which is written in a distinct Doric Greek dialect. (The above mentioned Aetolians and Acarnanians also spoke Doric and Macedonian names show Doric forms of Greek names)
There's toponyms, months of the year and personal names all of which show a Greek root. I believe there are 5 Illyrian names recorded but that is to be expected, Macedonia became less Greek the further north you went.
Then there's the list of 150 or so preserved words, most have been identified as Greek and do not appear to be mere borrowings as they show dialectal differences from Attic.
From what I have read, the majority of scholars believe that it was a form of Greek (Foxe, Hammond, Worthington, Cartledge) although some state it may have been a separate language under the same Hellenic branch.
A minority such as Borza believe that there is insufficient evidence to conclude yet still agree that that it was replaced by Koine. One thing that amuses me with the Macedonia controversy is the obsession with the Ancient Macedonian dialect. Wouldn't the fact that Macedonian was phased out by Koine Greek and not Slavic be a more relevant way to identify their descendants?