Most companies advertise-look in the job centre, local newspapers, etc for vacancies. Some shops also stick little posters in the windows or around the shop, so look out for these. Alternatively, you can walk into a shop and ask if they have any vacancies and/or for a job application, although you might not be guaranteed the job this way. Usually when a job is advertised they'll ask you to send in a CV and cover letter. Try big supermarkets, usually you can get an interview pretty quickly for these, but it is dependant on whether or not they have vacancies. Also, if you get rejected, don't give up trying-there'll be a job out there somewhere for you!
Good luck! I'm currently in the process of trying to get a new job (although I want permanent full time, not just a summer job, since I left college a while ago, and uni isn't for me). It's all fun and games!