Hello Betty, welcome to the Forums. In your GWT account when Google finds 404 errors on your site, they give you a list of the pages they cannot find. You should be able to check through that list and see if those are pages that do not exist and mark the checkbox next to that URL as "Fixed". Server errors are caused by faulty settings either by the host or in your own configurations such as .htaccess (if you're using an Apache server).

I would not be concerned about lists of pages that used to exist and are not on your site anymore. Those are supposed to return a 404 error, Google expects to see a 404 error if the page isn't there. Just mark them "Fixed" and forget about those. The other errors you should try to track down and fix. You should be able to see the URL that is giving the error so you know where to start looking.

Well I have done as you guided to me.I select all 404 and markup as fixed. Instant all pages gone,but after sometime some pages again appear.
Now tells me what have to do?

Same thing, every time the errors are found - until you can make them stop looking for pages that don't exist. When you are planning to remove or replace pages it's a good idea to noindex that page and make sure it is not in your sitemap anymore. After Google sees that you don't want that page indexed, they will eventually quit looking for it. Exceptions are when you maintain pages in your sitemap or have links either on your site or on other sites that link to those pages. If those links are found they will forever want to find those pages and you will see those errors. 404 errors in GWT are only a problem because they take time to remove. There is no penalty for having 404 errors, nearly everyone has them from time to time.

You don't have to do anything. Not everything listed in GWT as an "error" is a problem that you need to fix. Much of it is just informational. So "mark as fixed" really means "Yes, thank you, I know".

If you've intentionally removed a page, returning a 410 "Yes, I know it's gone, I took it away on purpose" will make google stop crawling a lot faster. (It doesn't seem to have any effect on bing.) They'll still report a "not found" error when they do crawl the URL, but you can just ignore that.

If there's an increase in 500-class errors, assuming that's what you meant by "server errors", that's probably worth investigating.

If you have recently moved the site from html to a CMS, like Wordpress, you'll likely be flooded with 404's. The way I deal with them (right or wrong) is to 301 all the recognizable pages. This might take weeks or months. Even though SF says you're site is responding 200 all around yet getting 4040's means that some site in the past may have linked to you using the old address.

Failing to 301 redirect missing established and backlinked pages will have you leaving valuable PR and link juice behind.

If the page is definitely dead, 410 it.
I moved a cms from one directory to another...then another! then I had WP set to https for a few days without knowing it. What a rats nest!

Right now I've got several wildcard 410's set. www.mydomain.com/m/* and www.mydomain.com/blog/* which I am hoping erases all knowledge of an old, moved WP installation. BTW, the CMS is now located in the root...but frome what G remembers, the other two might still exist.

My goal is to one day get a "Hey no errors in the last 90 days" message.

A fresh & clean site makes a HUGE difference. I installed WP on a clean domain yesterday. Today I'm ranking page 1 which is an incredibly fast uptake from G. The domain sat in a "under construction" one page state for almost 5 years, so it was properly primed.

Every time I get a WMT refresh, I have another batch to process...but it's slowly getting smaller.

Moral of the story, if you change your site a lot, and don't do 100% on the redirect job, you'll lose traffic.