You can usually find an article's DOI on the first page of the article, usually in the header or footer but sometimes at the end of the abstract or elsewhere.
If you can't find the DOI, try looking the article up in a service called Crossref. If you find your article in Crossref, it'll display the DOI. If you can't find your article, it may not have a DOI. This is fairly common for older articles. You'll just have to construct your citation without a DOI if the article you're using doesn't have one.