When you search this site, you could find quite a few answers to your question.
Personally, I would use LuaLaTeX. With LuaLaTeX you could just type Greek without any additional packages -- provided that you use a font that contains all the Greek characters (and accents) you are about to use. And: you don't need to learn new syntax or commands if you switch from LaTeX to LuaLaTeX.
For a document, that is completely in Greek:
% !TEX TS-program = lualatexmk
\documentclass[11pt,a4paper]{scrartcl}
\usepackage{fontspec}
\setmainfont[Ligatures=TeX]{Arial Unicode MS}
\begin{document}
πάντες ἄνθρωποι τοῦ εἰδέναι ὀρέγονται φύσει. σημεῖον δ᾽ ἡ τῶν αἰσθήσεων ἀγάπησις:
καὶ γὰρ χωρὶς τῆς χρείας ἀγαπῶνται δι᾽ αὑτάς, καὶ μάλιστα τῶν ἄλλων ἡ διὰ τῶν
ὀμμάτων. οὐ γὰρ μόνον ἵνα πράττωμεν ἀλλὰ καὶ μηθὲν μέλλοντες πράττειν τὸ ὁρᾶν
αἱρούμεθα ἀντὶ πάντων ὡς εἰπεῖν τῶν ἄλλων. αἴτιον δ᾽ ὅτι μάλιστα ποιεῖ γνωρίζειν
ἡμᾶς αὕτη τῶν αἰσθήσεων καὶ πολλὰς δηλοῖ διαφοράς. φύσει μὲν οὖν αἴσθησιν ἔχοντα
γίγνεται τὰ ζῷα, ἐκ δὲ ταύτης τοῖς μὲν αὐτῶν οὐκ ἐγγίγνεται μνήμη, τοῖς δ᾽ ἐγγίγνεται.
\end{document}
And if you need both English and Greek:
% !TEX TS-program = lualatexmk
\documentclass[11pt,a4paper]{scrartcl}
\usepackage{fontspec}
\setmainfont[Ligatures=TeX]{Times New Roman}
\newfontfamily\greekfont[Scale=MatchUppercase,Ligatures=TeX]{Arial Unicode MS}
\newcommand{\textgreek}[1]
{\bgroup\greekfont{#1}\egroup} % Greek text
\newenvironment{greekpar} % Greek paragraph
{\greekfont}{}
\begin{document}
This is English with some Greek: \textgreek{γέγονεν}.
\begin{greekpar}
πάντες ἄνθρωποι τοῦ εἰδέναι ὀρέγονται φύσει. \textrm{And this is a Greek paragraph with some English.} σημεῖον δ᾽ ἡ τῶν αἰσθήσεων ἀγάπησις: καὶ γὰρ χωρὶς τῆς χρείας ἀγαπῶνται δι᾽ αὑτάς, καὶ μάλιστα τῶν ἄλλων ἡ διὰ τῶν ὀμμάτων. οὐ γὰρ μόνον ἵνα πράττωμεν ἀλλὰ καὶ μηθὲν μέλλοντες πράττειν τὸ ὁρᾶν αἱρούμεθα ἀντὶ πάντων ὡς εἰπεῖν τῶν ἄλλων. αἴτιον δ᾽ ὅτι μάλιστα ποιεῖ γνωρίζειν ἡμᾶς αὕτη τῶν αἰσθήσεων καὶ πολλὰς δηλοῖ διαφοράς. φύσει μὲν οὖν αἴσθησιν ἔχοντα γίγνεται τὰ ζῷα, ἐκ δὲ ταύτης τοῖς μὲν αὐτῶν οὐκ ἐγγίγνεται μνήμη, τοῖς δ᾽ ἐγγίγνεται.
\end{greekpar}
Isn't that quite nice? \textgreek{εὕρηκα!}
\end{document}