Q: I have trouble updating Mac OS El Capitan in my MacBook Air (mid 2011) laptop. Any help would be appreciated.

What happens when you try?

boot into safe mode

Try safe mode if your Mac doesn't finish starting up - Apple Support

close app store (if its open)

open terminal

type

open $TMPDIR../C/

delete the folder

com.apple.appstore

(this will delete all unfinished downloads from the store, it will not affect completed and installed ones)

open app store

download the OS

if the issue persists see this article

Recommended settings for Wi-Fi routers and access points - Apple Support

and you can also download the OS for free from the App store but with the 10:00AM Apple conference this AM you may want to secure El Capitan in your Apple account in the event Apple releases a new public OS and El Capitan is no longer available unless you already have it in your account.

You can try Jimmy's suggestion. But, if you already downloaded it and it started to install and failed, you might have something installed on your Mac that is preventing the installer from running correctly.

If Jimmy's suggestions don't work, try running this program and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. On the screen with Options, please open Options and check the bottom 2 boxes before running. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown.

Etrecheck – System Information