There is a range of input systems available for Mac and for Windows. Many of these are system keyboards: just like one may switch the keyboard of a computer between a US, UK, Dutch, etc. keyboard, with slight differences (e.g. the position of @, ”, etc. — the differences reside in which code is produced by which keystroke), so too your computer system may be set to a ‘polytonic’ Greek keyboard, which allows for the input of Greek with a full range of diacritics (accents and breathings). Typically, Polytonic Greek keyboards involve the use of ‘deadkeys’, keystrokes which do not themselves produce a symbol, but modify the output produced by the following keystroke (for instance, in the GreekKeys keyboard, pressing the key ‘1’ produces no character, but when it is followed by pressing ‘a’ it produces ἀ). Windows and Mac computers come pre-installed with (free) polytonic Greek keyboards, but these are on the whole difficult to use, in that they require memorizing different dead keys spread out across the keyboard for every possible combination of diacritics (thus producing each of ἀ, ἁ, ά, ὰ, ᾶ, ἄ, ἂ, ἆ. requires memorizing a different deadkey placed without clear logic across the keyboard). The GreekKeys system, produced and maintained under the auspices of the American Philological Association, also utilizes system keyboards with individual deadkeys, but these are positioned on the keyboard in a much simpler fashion. Another (commercial) Greek keyboard is LaserGreek. Various other keyboards exist: some may be found here, or simply by searching online for ‘Polytonic Greek keyboard’. Universities will often provide students with a license for one of them.
Some system keyboard solutions which allow for more functionality, particularly the combination of deadkeys (so that only two deadkeys need be memorized for ἀ, ά, and ἄ), require the installation of software on a Windows computer. The best example is a package called Keyman, for which various polytonic Greek keyboards have been produced. On Mac computers, combinations of deadkeys are always possible, provided that a keyboard allowing for such combinations is used.