This might be a really trivial question, but I've been writing Java programs at my school and I just found out that I can create websites with Java as well.
You are asking a few different questions...
The simplest way to start making websites with Java is to use JSP. JSP stands for Java Server Pages, and it allows you to embed HTML in Java code files for dynamic page creation. In order to compile and serve JSPs, you will need a Servlet Container, which is basically a web server that runs Java classes. The most popular basic Servlet Container is called Tomcat, and it's provided free by The Apache Software Foundation. Follow the tutorial that cletus provided here.
Once you have Tomcat up and running, and have a basic understanding of how to deploy JSPs, you'll probably want to start creating your own JSPs. I always like IBM developerWorks tutorials. They have a JSP tutorial here that looks alright (though a bit dated).
You'll find out that there is a lot more to Java web development than JSPs, but these tutorials will get you headed in the right direction.
This is a pretty subjective question. PHP and Java are just tools, and in the hands of a bad programmer, any tool is useless. PHP and Java both have their strengths and weaknesses, and the discussion of them is probably outside of the scope of this post. I'd say that if you already know Java, stick with Java.
MySQL is better suited for web applications, as it is designed to handle many concurrent users. You should know though that Java can use MySQL just as easily as PHP can, through JDBC, Java's database connectivity framework.
Also be advised, that while Java is in general very beginner friendly, getting into JavaEE, Servlets, Facelets, Eclipse integration, JSP and getting everything in Tomcat up and running is not. Certainly not the easiest way to build a website and probably way overkill for most things.
On top of that you may need to host your website yourself, because most webspace providers don't provide Servlet Containers. If you just want to check it out for fun, I would try Ruby or Python, which are much more cooler things to fiddle around with. But anyway, to provide at least something relevant to the question, here's a nice Servlet tutorial: link
While a lot of others should be mentioned, Apache Wicket should be preferred.
Wicket doesn't just reduce lots of boilerplate code, it actually removes it entirely and you can work with excellent separation of business code and markup without mixing the two and a wide variety of other things you can read about from the website.
Look into creating Applets if you want to make a website with Java. You most likely wont need to use anything but regular Java, unless you want something more specialized.
I'll jump in with the notorious "Do you really want to do that" answer.
It seems like your focus is on playing with Java and seeing what it can do. However, if you want to actually develop a web app, you should be aware that, although Java is used in web applications (and in serious ones), there are other technology options which might be more adequate.
Personally, I like (and use) Java for powerful, portable backend services on a server. I've never tried building websites with it, because it never seemed the most obvious ting to do. After growing tired of PHP (which I have been using for years), I lately fell in love with Django, a Python-based web framework.
The Ruby on Rails people have a number of very funny videos on youtube comparing different web technologies to RoR. Of course, these are obviously exaggerated and maybe slightly biased, but I'd say there's more than one grain of truth in each of them. The one about Java is here. ;-)
Source: Stackoverflow.com