Note that this is mostly targeted to post-doctoral researchers and PhD students but is less important for students asking to join for a trainings period.
• A motivation letter or motivation statement (also called a cover letter)
• An up-to-date curriculum vitae (CV)
• Contact information for references
• A publication list (can be part of the CV)
• (Language certificates might be needed for doctoral students)
Here you need to clearly explain why you would like to join our research team. Look at our publications, webpage and other available information.
Importantly, if you are unsure and you would need more information about the position, the research group, or the work environment then send an email asking for more information. This is not impolite and actually gives a good impression since you are showing interest.
Read the announcement carefully! I will invariably ask for pdf documents, not doc files
Use an email address based on your name. If you are not currently employed and therefore have an official email address (or you don’t want or cannot use that for whatever reason) there are plenty of free options.
Some more links with info on applications:
http://thesiswhisperer.com/
http://thesistips.wordpress.com/