After having summer internships in a number of marketing-related companies (McCann-Erickson, Bristol 2010 and Warc, London 2011) I thought I'd share some advice on how to make the most of an internship. After all, internships are not only highly competitive to get, they don't last forever.
Write Down Every Task You're Given, As Soon As You're Given It.
This is my strongest piece of advice. As an intern, you'll probably be asked to do a variety of tasks. Even by the end of the day, you may not remember every task you were given, especially if they were a number of short tasks. So I write down every task in my notebook before I begin it. That evening, I write a more detailed account of what was involved. It will take less than a minute of your time in the office and a couple more later on the evening. But what you gain is a bank of examples that can be used for your CV and examples of using specific skills for interviews. If you leave it all to the end, you'll probably struggle to remember some of the smaller tasks, but these could be brilliant examples of your skills.
In industries where internships are common, its very likely that your senior colleagues have experience interning. If there's someone in the company who is in a role you are interested in when you graduate, ask them how they got there and what they'd recommend you doing (e.g. is a postgraduate degree particularly beneficial?). Or if you happen to know the people who interview candidates for such a position ask what will make you stand out on paper or typical interview questions. This will probably benefit you far more than a careers adviser at university ever would.
Some internships are more flexible than others. If you're in an internship which hasn't been meticulously planned from start to finished, you may be asked what you'd like to get involved or what your career goals are, and given tasks to match. You'll probably only get asked this once (if it all), so if you do, make sure you give an honest answer. Equally, if you feel you are repeatedly being given tasks which don't match the job description, you should always speak up. It's obviously unprofessional to refuse a task because you think it's boring or would rather be doing something else, but if you do find yourself stuffing envelopes day-in-day-out when that wasn't what you signed up for, it's unlikely anything will change unless you speak up.
I've put this as the last piece of advice because I'm currently sceptical of whether LinkedIn actually benefits getting a job. However, it can be useful in staying in touch with people that you've met in your working life as an intern, although I'd argue that LinkedIn is probably more useful in B2B than if you're looking for a graduate/permanent position. Still, getting a positive recommendation for all to see can't hurt.