First you need a basic knowlendge of how the net works

Server
Client
POST
GET
Ports: 21
80
etc.
Protocols: TCP
UDP
HTTP
HTTPS
FTP
SMTP
p2p
etc.

Google all these words

Then...

WEB DESIGNING
The way a web page looks, you'll be able to make sheet content pages

HTML [3 days to learn]
a web page structure like words, lists and tables
codecademy.com

CSS [4 days for me... I was really bored]
add colors, backgrounds and alot of fancy things to your page
codecademy.com

HTML DOM (this after you learnt Javascript) [3-4 days 1 hour a day, making some tests at jsbin.com]
Yu need this to animate your pages, someone click a button and the words change color (a simple example)
I use it to send forms with AJAX (we will cover these things then)
http://www.w3schools.com/htmldom/default.asp

WEB DEVELOPMENT
You'll be able to send emails, store things in a database, build alot of services, process payments (with a payment gateway API...we will cover the API stuff then) etc. etc.

Javascript [2-3 weeks, I was really bored because I knew it is not important to make a project]
You need it to learn HTML DOM, this is the only way I use it
learnsrtreet.com (It has only the beginner course)
codecademy.com

I had some problems with a codecademy exercise so I moved to learnstreet. When I realized that it cover only the beginner course I moved again to codecademy. I made all the learnstreet course so I was able to finish that problematic exercise .

PHP [2 weeks]
Well, this is all you need to make your project come true
http://www.w3schools.com/php/default.asp

MySQL [1 week]
Make your database and use PHP to talk with him
mysqltutorial.org

I use PDO prepared statements to send data to my database, you find everything you need to know about them at
mysqltutorial.org/php-mysql/
net.tutsplus.com/tutorials/php/pdo-vs-mysqli-which-should-you-use/
http://net.tutsplus.com/tutorials/php/pdo-vs-mysqli-which-should-you-use/

1 project, 1 API....
You need them if you want communicate with payment gateway sites, with sites that provide telephone services like VOIP or give you the possibility to send SMSs online etc. etc. I send the data to my "service provider" with PHP cURL
http://php.net/manual/en/book.curl.php

Find the API that fits your needs here
programmableweb.com/apis/directory

Tips for your project

I use CSS frameworks to make nice web-pages
awwwards.com/what-are-frameworks-22-best-responsive-css-frameworks-for-web-design.html

I send data from my HTML forms with Javascript using AJAX
http://www.w3schools.com/ajax/default.asp

And then I process the data with a PHP page (I use the same page where the form is)
http://www.w3schools.com/php/php_ajax_php.asp

I always make a token to secure my forms from hackers
css-tricks.com/serious-form-security/

Hope you'll find these info useful