Learn German: Ich komme aus Spanien.

You would use woher (from where). The full question is Woher kommst du? (Where do you come from?). Woher asks about your origin, and we answer it using the preposition aus (from/out of) followed by the place.

Can I use von instead of aus to mean "from" here?

Not for countries or cities! When you talk about your geographical origin, you always use aus in German. You use von when coming from a person or a specific activity, but for places like Spanien, it is always aus.

Why does the verb end in -e (komme)?

In German, verb endings change to match the subject. The base form of the verb is kommen (to come). Because the subject is ich (I), we drop the -en and add an -e, giving us ich komme.

Why isn't there an article (like a word for "the") before Spanien?

Most countries in German, including Spanien, don't use an article when you say you come from them. You just use the name of the country directly after aus. You will eventually learn a few exceptions (like Switzerland or the USA), but Spain doesn't need one.