Internships are undertaken while you study, or after you graduate. Some might be advertised, or you could try approaching organisations directly.
Larger companies might run graduate schemes that provide training while you work
A lot of work experience in this area is informal
Researching and finding contacts may be key to securing work experience. Try to find the name of the person responsible.
Apart from anything else, it will show you have the skills and tenacity that you will need if you want to be a journalist. You can use printed resources, the web, social media...