Well windows services is not a big deal. It is just running by windows instead of an user. So what you might want to do is;
*Use a try-catch block where you start your process or your service and log the exception as if throws it.
*You can create a global error handler which logs everything your service does.
Some detailed info you can find here;
Exception Management Rules[
^]
and some more articles about it;
Exception Handling Articles[
^]
And a global exception handler;
Global Exception Handler Code for C#[
^] ( this is an extra, since you havent identified a language, I thought it might be useful..)
Good luck.