I'm not sure how to know which space I need to set a document in Adobe Illustrator CS5 when I want to create a six-sided DIN A4 folder-flyer. Is there a template somewhere out there that I can use? Or how can I configure the document so that the flyer will be I want to create this flyer and let it get printed by a printing shop, and we've only got Illustrator in our company - and I didn't work with Illustrator too much before. I hope this Stackexchange site can help me even if I don't have much experience with CS5.
In AI CS5, you can select
File > New From Template and under the Japanese section, in the Marketing folder, you'll find that j-brochure1.ait is an A4 template for a trifold. Just delete the artwork and keep the fold marks. If you have a European version of AI, you may find that the regular Blank brochure template is A4. On my US version, it's US Letter size, which wouldn't be much help to you. The folds are not evenly spaced, so there's an art board for the "outside" and one for the "inside" of the piece.
There are many companies that offer printing services to "the trade" and consumers through their websites. It's become a very common business model for companies offering standard commercial jobs such as postcards, fliers, booklets, etc. Every one I have seen has templates on its website available for download, and the kind of trifold you describe is a very standard item so you should have no trouble finding numerous templates. The print shop you are planning to use may also have one, so it's worth asking them. (Rule: Always ask your printer!)
A jpeg can be dropped into Illustrator and the artwork built on it, or you may find a native Illustrator or EPS template.