Whereas you should start planning your internship abroad around 1 year beforehand, applications for internships in countries outside Europe need only be submitted about 6-7 months in advance. Applications for European internships are less urgent – no visas are required for EU citizens within Europe – but you should not leave it too long or the positions you are seeking could be filled.
One exception to this general rule are applications to international organisations, German representations abroad (embassies, consulates) and so on which can have application deadlines of up to one year before the internship starts.

Always keep one thought in mind: DON’T BE DISCOURAGED!
You may not be successful first-off, you may make a number of applications and not receive an offer – but it’s vital that you stick with it! If you can show commitment and staying power, you will ultimately be rewarded. 

If the company or organisation to which you are applying does not specify any particular documents, then your application should consist of a covering letter and a CV (résumé). These should be written in the language of the host country or at least in English. Just translating a German application is not enough – it’s all about giving a concise yet detailed presentation of your own knowledge, skills and abilities.  No german umlauts or special characters. You should also be aware of typical do’s and don’ts for certain countries. Lots of examples and explanations can be found on the internet (e.g. Staufenbiel Institut [only available in German], [only available in German], [only available in German]).

Your covering letter should point out what you have already learned or what work you have done, exactly why you think the internship at this company or laboratory of this university abroad will provide the practical experience you are looking for, and what value-added you can offer the host organisation. It should make clear that you have already done your ‘homework’ on the company or research field at the foreign university. The letter should be addressed to an actual contact.

If you apply for an advertised job offer, you have to respond to the required knowledge and skills. 
Your CV (résumé) should be broken down into several points, starting with your personal data (here again, be aware of do’s and don’ts for different countries, e.g. no date of birth for the USA) moving on to education, work experience, skills (software, languages etc.), achievements/awards, (extracurricular) activities, references.  Other points may also be relevant depending on your personal experience and development, so avoid blindly following a template!
Individual points should be presented in reverse chronological order, starting with the most recent academic achievement, latest position etc., and working back in time.

Unlike a German CV, your CV should not be signed or dated.

Applications for an internship should always be transmitted electronically as a PDF file from a proper and serious email address (e.g. the students email address at OTH Regensburg). Ideally, this is done to your direct contact within the host organisation, or if this is not possible, to the relevant HR department or through the organisation’s online application portal.

The covering letter and CV/résumé should be converted to a PDF file and sent as an attachment to the email. The PDF should not be bigger than 2 MB.

It is recommended to follow up on your email about 1 to 2 weeks after you first submitted it, as this will reflect the seriousness of your application – and it’s entirely normal in many countries.

If you are offered an interview, it will usually be by telephone. You shouldn’t be afraid of this, especially of speaking in a foreign language – no one will be expecting perfect linguistic skills. The focus of the interview will often be on the actual work involved at the host organisation, and here again, the internet offers lots of ways in which you can prepare for your interview.