Finding work experience is a tricky business. It can involve a little forcefulness, a little boasting, and a little persuasion; in the right ratio these can be a killer combination.
If you have the opportunity, be picky with where you apply to for work experience. At the end of the day, there really is no point in applying to work somewhere if you aren't totally committed in your heart to that position or that workplace. What if you get the spot and hate it? You're wasting your own time, the business' time, and you've also stolen away the opportunity from someone who might have really, really wanted that placement. Being a little fussy is not always a bad thing, especially if you're looking for work experience whilst you are still in education- it isn't like you have bills to pay, just life experience to gain so you can (both metaphorically and literally speaking,) afford to set your sights at the top.
Once you're sure of the kind of work experience you want, start doing your research. If you don't have a car, look for places nearby that are accessible by train or bus. Check out if there are any specifications that must be handled before you can apply, look to see if there are particular times of the year when placements are available, make sure that this company even does the kind of thing that you're interested in! And if any of these basic questions cannot be answered on their website, then email in. A little email or phone call won't hurt; the first point of contact can be the hardest, but don't be shy. Confidence is what will propel you forwards. I have a friend at University who has the attitude that if you sit around and wait long enough, then the opportunities will come to you. I will tell you now, that he has not got a high success rate to go with this mantra.
Once you've got yourself noticed, make sure you are not forgotten. Most companies have bigger things to think about than work placements and can forget who has contacted them and when. Regular, but well spaced and practical emails to your person of contact at the business will make sure they know you are serious and that you are still interested in working with them. A keen attitude and strong work ethic will assure them you are the kind of candidate that they're looking for.
Finally, as I have always said in any of my blog posts; just be confident in yourself. Make yourself believe you are the right person for the job, and make it a self-fulfilling prophecy. Take a look at our internships: http://www.graduate-jobs.com/internships_and_work_placements