Sure. To start working on browser games, you need some sort of website. You can get a free host, pay for one, or just run a server on your local computer. Local computer is probably best, but it's a much easier set up to just get one from a company online.

I have no idea if this website host is good: http://www.000webhost.com/, but it has what you need; database access and php installed. If it forces you to go through some crap; try and find another host, as I am in no way sure if this is best, it just came up first on google when I tried "free web host php mysql".

Once you have that set up, you can use phpMyAdmin, or whatever their built-in database management system is to enter those queries that he uses:

CREATE TABLE users (
id int NOT NULL AUTO_INCREMENT,
username varchar(250),
password varchar(50),
PRIMARY KEY(id)
);
That stuff. You can enter it using whatever database system they're using. You might have to root around a little in the website's control panel before you find access to it, but there's like a 99% chance that they'll have one.

Before you start using that, if you're not familiar with the basics of html and how a webserver works, you should probably learn that first. You can find a basic HTML tutorial here: http://www.w3schools.com/html/default.asp

Once you understand basic HTML and webserver workings, as well as how to access the database, you should be able to somewhat understand what he's saying; hopefully enough to get started.