I directly gave cookies of an existing connection to wget with --no-cookies and the Cookie HTTP request header. In my case it was a Moodle university login where logging in looks more complex (using multiple requests with a login ticket). I added --post-data because it was a POST request.
For example, get all Moodle users list:

wget --no-cookies --header "Cookie: <name>=<value>" --post-data 'tab=search&name=+&personsubmit=Rechercher&keywords=&keywordsoption=allmine' https://moodle.unistra.fr/message/index.php

If you need it for one time use, you can log in via browser and copy needed headers afterwards:

Use "Copy as cURL" in the Network tab of Developer Tools (reload the page after opening) and replace curl's header flag -H and --data with wget's --header and --post-data.

I had the same problem. My solution was to do the login via Chrome and save the cookies data to a textfile. This is easily done with this Chrome extention: Chrome cookie.txt export extension.

When you get the cookies data, there is also an example on how to use them with wget. A simple copy-paste command line is provided to you.

You don't need cURL to do POSTed form data. --post-data 'key1=value1&key2=value2' works just fine. Note: you can also pass a file name to wget with the POST data in the file.

I wanted a one-liner that didn't download any files; here is an example of piping the cookie output into the next request. I only tested the following on Gentoo, but it should work in most *nix environments:

wget -q -O /dev/null --save-cookies /dev/stdout --post-data 'u=user&p=pass' 'http://example.com/login' | wget -q -O - --load-cookies /dev/stdin 'http://example.com/private/page'
(this is one line, though it likely wraps on your browser)

If you want the output saved to a file, change -O - to -O /some/file/name

If they're using basic authentication:

wget http://username:password@www.domain.com/page.html

If they're using POSTed form data, you'll need to use something like cURL instead.

A solution which uses lynx and wget.

Note: Lynx has to have been compiled with the --enable-persistent-cookies flag for this to work

When you want to use wget to download some file from a site which requires login, you just need a cookie file.
In order to generate the cookie file, I choose lynx.
lynx is a text web browser.
First you need a configure file for lynx to save cookie.
Create a file lynx.cfg. Write these configuration into the file.

SET_COOKIES:TRUE

ACCEPT_ALL_COOKIES:TRUE

PERSISTENT_COOKIES:TRUE

COOKIE_FILE:cookie.file

Then start lynx with this command:

lynx -cfg=lynx.cfg http://the.site.com/login

After you input the username and password, and select 'preserve me on this pc' or something similar. If login successfully, you will see a beautiful text web page of the site. And you logout.
The in the current directory, you will find a cookie file named as cookie.file. This is what we need for wget.

Then wget can download file from the site with this command.

wget --load-cookies ./cookie.file http://the.site.com/download/we-can-make-this-world-better.tar.gz

Example to download with wget on server a big file link that can be obtained in your browser.

In example using Google Chrome.

Login where you need, and press download. Go to download and copy your link.

Then open DevTools on a page where you where login, go to Console and get your cookies, by entering document.cookie

Now, go to server and download your file: wget --header "Cookie: <YOUR_COOKIE_OUTPUT_FROM_CONSOLE>" <YOUR_DOWNLOAD_LINK>