There is a proper and responsible way of how to delete a page from your personal web site that does not impact negatively on the surfing experience of your readers. You don't want your readers to be clicking on a URL on the Google search page results just to be told that the page cannot be found. That negligence on your part is simply not acceptable.
Removing a page from your personal web site is unlike deleting a file from your computer where you simply get rid of the files that you no longer need. Your page may have been indexed by search engines so you have to make sure that you will be able to remove the URL of your page from the index of the search engines.
Before deleting a page from your personal web site, be sure to check first if the URL of the page is in the index of the search engines. For Google, just go to the Google search page and type the word info followed by a colon and then followed by the URL of the web page that you are deleting. If the URL is indexed by Google, save the URL somewhere where you can get it back later. If not, then you can just go ahead and delete the web page.
After deleting the page, you can now request Google to remove the page's URL in the Google index. You do this step by making a page removal request within or outside of the Google Webmaster Tools. You can search Google for the web page where request for removal is made. You will need a Google email address if you will be requesting the removal outside of Google Webmaster Tools. It takes a number of days before the URL's data on the index are removed and you can monitor the status of your removal request.
If you would be including a page that has the same title and URL as the one that you have just deleted, you should delay posting the replacement article until after the old web page had been removed from the search engine's index. If the citations of the old page is still present at the search engine's index, then your article will be seen as duplicate and may still be indexed but the old citation may be the one that will be shown on the search engine's search results page. And when the user clicks on the old citation, she will be presented with a page not found result.
If you are making a big change on the page and you even plan to change the title, it would be better just to delete the whole page and replace it with a new one. We know that Google looks at the domain name when assessing the relevance of web page but I'm not sure if a search engine friendly file name is included in the assessment of page relevance. In any case, it would be best to have a file name that is consistent with the title of the page.
If you have already deleted a number of pages from your personal web site without saving the URLs of those pages and requesting that they be removed from the search engine's index, you may still be able to retrieve the URLs if you want to remove them from Google's index. I have made this mistake in the past and deleted a number of pages from one of my Blogger blogs. But when I tried subscribing to the feeds of that particular blog using the Google Reader, I found out that the web pages I deleted were still in Google's index. That gave me an opportunity to request for their removal.
So the lesson that I want to point out is that simply deleting a page from your personal web site is not a good and responsible practice. To prevent your readers from having to deal with page not found responses, make sure that you also remove the web page's citations on the index of the search engines.
Read an article on how you can permanently remove your web page from the Google search engine at: http://laptopwriting.blogspot.com/2011/11/how-you-can-permanently-remove-your-web.html.