The KOMA-Script letter class scrlttr2
is very customizable and provides support for DIN 676/5008 out of the box (p. 195):
DIN
parameter set for letters on A4-size paper, complying with German standard DIN 676; suitable for window envelopes in the sizes C4, C5, C6, and C6/5 (C6 long).
DINmtext
parameter set for letters on A4-size paper, complying with DIN 676, but using an alternate layout with more text on the first page; only suitable for window envelopes in the sizes C6 and C6/5 (C6 long).
(Even though DIN 676 has been superseded by DIN 5008 in 2011, the regulations for the layout of business letters have almost kept the same, only one dimension has been relaxed a bit. Hence, the DIN 676 layout adheres to DIN 5008.)
Parameter sets are simply passed as options to the class. The following shows a minimalistic letter:
\documentclass[version=last,DIN]{scrlttr2}
\usepackage[english]{babel}
\begin{document}
\begin{letter}{%
Joana Public\\
Hillside 1\\
12345 Public-City%
}
\opening{Dear chairman,}
the last general meeting was about one year ago.
I want to remind you, that the constitution of our club advises you to make a general meeting every six month.
Because of this I expect the executive board to detain such a meeting immediately.
\closing{Expecting an invitation}
\end{letter}
\end{document}

In fact, the DIN
settings are even loaded as a default, so it is not necessary to pass them explicitly. For further customizations, please take a look into the Manual, which is available in German and English.
Only available in German is the extended manual as a printed book, which is supposed to provide specifically more customization examples for the letter class.
article
class works for letters as well.