A good idea is to try and enter competitions etc. you may find if your work stands out you might attract somebody, for example in the 3rd year my Mum was studying Illustration, she entered a competition to illustrate a poster for a theatre production, she won and the theatre company that funded the competition gave her 3 more jobs to do. Freelance is a good way to get yourself known, apparently, but it seems the hard bit is starting to find freelance work to do.
As I am doing a Writing course, I will need to get my prospects out, what I plan to do is to send work to magazines, competitions and try to get freelance work whilst I am university, so when I leave university and apply for that job I have a nice CV and a decent portfolio, as well as my 'getting involved' in university life I hope will prove useful too (such as doing the radio show). Things like that are suppose to impress employers. It also helps to have a bit of published work to flash in their faces.
Connections do help you get a job, of course no one is as lucky as someone to say 'I like you, you're hired', freelance work with a specific company can help, some like Future publishing like freelance work to be done for them and of course their actual job applications require a qualification and/or published pieces, so in turn in this example (which is geared towards writing, but same principle should apply) they know you name, you could show that you've got some work published in their magazines, if they're satisfied they'll hire you.
And of course researching the companies doesn't do any harm either.
Generally, just have a lot on your CV and have something about you to sell to them that stands out and is relevant for what you're applying for. And more importantly, don't be fussy like my sister, one thing you don't like doing could well be the step to doing something you really enjoy.
I love Nancy DrewG, but not insert brain here