Forms, PHP to Paypal? - PHP confusion/clarity

Trying to learn, and literally got stumped.. not even sure if my assumption is correct or not...

I have been trying to learn and play around with this on my own and the reference I have through what I want to learn is this: purenailbar.com/gifts.html
Please correct my assumptions.

So...

Step One:

* it is an HTML page with a form
* it uses jquery validator
* if you don't input anything, validator makes you fill it in
* hit submit

Step Two (a) - reach gifts_review.php :

* This is a php form(?)
* You pass Step One (filled up requirement)
* Review the the form to make sure...
* Hit the "paypal button"

Step Two (b) - reach gifts_review.php:

* This is a php form(?)
* You 50% pass Step one (because you did not select the type of service or the "dollar amount"
* You have to hit back to type in Dollar # or select service
* Hit "submit", review gifts_review.php, then hit "paypal button"

Step Three:

* You get directed to the Paypal payment/section
* Login and pay for it, etc.
* After paying, it gets processed
* Then you get redirected after paying.. back to their official websit e(non-paypal) thank-you or payment received page.

Step Four:

* You login to your email address
* Check to see your receipt..
* Paypal Email 1 - receipt of payment
* Paypal Email 2 - the information you wrote on the form(?)

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My questions:

* Probably a dumb question... how can you have a html form then to a php form?
* is the php review form a script that "memorizes" the form? Or this is an option that Paypal already has that I am not aware of?

Personally, I only got up to step one (which anyone can get through, lol).. I got stumped on the php part.. I'm new to it.. and don't know how to write script for it to (validate??) obtain the data from the from on the html page.

And played around with the code paypal gives when you select a buy now/donation button.. and played around with customizing the page too, which was successful (and also tutsplus has it too so thats where I also learned).. When I saw this approach, I thought it was cool.. LOL.