If an article is obviously unnecessary, just delete it. (To delete a page, edit it and remove all of its content.) For example:
A page that has been completely replaced by a different page
A page that describes something that no longer exists, and there's no pressing reason to keep a historical record
If it's unclear whether a page is necessary, add it to the list labeled “Candidates for Deletion” below.
Make a good faith effort to identify the relevant committee (or if no committee, those that might care most about the page) and discuss with them if the page is necessary.
If no specific stakeholders are immediately apparent, make a more general post on Talk & Slack soliciting any input on the potential deletions.
Allow sufficient time (1-2 weeks) for potential issues to be raised, discussed, and addressed. Aim for consensus, but if there's disagreement, consider alternatives to meeting everyone's goals, not just black-and-white outcomes.
If the general conclusion is to delete the page, delete it and remove it from the Candidates for Deletion list.
If the general conclusion is not to delete the page, figure out why it was suggested for deletion and try to address that (e.g. if the page is outdated, try to update it).