\documentclass{article}
\usepackage[polutonikogreek,english]{babel}
\begin{document}
This is a test of typesetting ancient Greek with LaTeX:
\selectlanguage{polutonikogreek}
>En >arq~h| >~hn <o l'ogoc\dots
\selectlanguage{english}
Here's the correspondance between "greek" and "latin" encoding for TeX:\\
\texttt{a b g d e z h j i k l m n x o p r s t u f q y w c} \\
\selectlanguage{polutonikogreek}%
a b g d e z h j i k l m n x o p r s t u f q y w c
\selectlanguage{english}
A simple example how to get accents and spirits: \\
\texttt{'a `a ~a >a <a a| >~a| "i "'i} \\
\selectlanguage{polutonikogreek}%
'a `a ~a >a <a a| >~a| "i "'i
\begin{tabular}{cccccccc}
& & & & & & & \\
& & & & & "U & & "u \\
& & & & & & & \\
& & & & & & & \\
"~ & & & "' & "` & & & \\
( & ) & * & + & , & - & . & / \\
0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
8 & 9 & : & . & < & = & > & ; \\
<~ & A & B & <` & D & E & F & G \\
H & I & J & K & L & M & N & O \\
P & Q & R & S & T & U & <' & W \\
X & Y & Z & [ & >~ & ] & >' & >` \\
` & a & b & c & d & e & f & g \\
h & i & j & k & l & m & n & o \\
p & q & r & s & t & u & & w \\
x & y & z & & | & & ~ & \\
`a & <a & >a & <`a & `a| & <a| & >a| & <`a| \\
'a & <'a & >'a & >`a & 'a| & <'a| & >'a| & >`a| \\
~a & <~a & >~a & & ~a| & <~a| & >~a| & \\
`h & <h & >h & <`h & `h| & <h| & >h| & <`h| \\
'h & <'h & >'h & >`h & 'h| & <'h| & >'h| & >`h| \\
~h & <~h & >~h & & ~h| & <~h| & >~h| & \\
`w & <w & >w & <`w & `w| & <w| & >w| & <`w| \\
'w & <'w & >'w & >`w & 'w| & <'w| & >'w| & >`w| \\
~w & <~w & >~w & & ~w| & <~w| & >~w| & \\
`i & <i & >i & <`i & `u| & <u| & >u| & <`u| \\
'i & <'i & >'i & >`i & 'u| & <'u| & >'u| & >`u| \\
~i & <~i & >~i & "I & ~u| & <~u| & >~u| & "U \\
`e & <e & >e & <`e & `o| & <o| & >o| & <`o| \\
'e & <'e & >'e & >`e & 'o| & <'o| & >'o| & >`o| \\
"i & `"i & '"i & ~"i & "u & `"u & '"u & ~"u \\
a| & h| & w| & <r & >r \\
\end{tabular}
\end{document}