First off, welcome to the forum!
In Safari, tap on the icon that looks like an open book. At the top of the drop-down that'll appear, you'll see a line called "Reading List." Select it and it'll open to show all the articles you've put in the Reading List.
Once you are there, swipe to the right on any article you want to delete and you'll get a red Delete button. Press the button and the article is gone. Rinse and repeat for all the articles you want to delete.
Marilyn
Thanks for that reply. Not sure why they didn't make it more obvious, like deleting a regular bookmark. But it was driving me crazy. How is the average person supposed to know this? Thanks again, you removed a straw from this camel's back!