How to delete old links showing up in search results

Hi there, I redesigned my website myself and updated all urls and content from the previous web designer. I tried to index my website on google but it still shows all the links from previous content that are no longer available. Now the main link comes up in the results, but the sub links below all have page not found. How do I update and delete these sub links? I’ve temporarily removed a few of these links but there are over 500 pages to do that for and I don’t know if thats just temporary and not permanent fix.

I am brand new to SEO so please explain in simple terms if you can. Thank you!!