Hi Thomas,
You have to be a little bit more specific on that. From my knowledge, there
is no single source which can tell you where to find the records you're
looking for, it strongly depends on what type of record from which region
you are looking for.
First, in the (old) state of Württemberg, there were no civil records in
1810. If you're looking for birth data, you'll have to stick to church
records. Where to find the church records obviously depends on the religion
(catholic or evangelic/lutheranian) and also the region of origin.
In some areas within Württemberg, the church records are still in the
churches, in others, you'll find the records in the church archives.
In most archives again, you need to have an appointment, as they are very
busy, so it might be advisable to organise that well in advance, while you
are still at home.
Concerning the military service in Württemberg: a compulsary military
service was implemented in 1806, but with considerable exceptions. Thus your
ancestor did not necessarily serve in the military.
Census: the first census in Württemberg was conducted in 1834 by the
"deutscher Zollverein". I have no idea what happened with the data obtained
from the first couple of censuses, I presume it was lost in time.
Also, most of the draft lists are lost.
Rudolf