How do I make a blog like Startlet's website? (www.``````````````)

I'm assuming you mean what utilities can you use? Starlet uses b2 (http://cafelog.com). Other free blog utilities include Greymatter (http://noahgrey.com/greysoft), Movable Type (http://movabletype.org), and WordPress (http://wordpress.org). These all require a host that supports PHP and MySQL.

How do I know if my host supports PHP and MySQL?

Also, Once a make a blog, how do i get it onto my site?

Your host will list what they offer on their signup page. Most free hosts don't support PHP/MySQL, but some do. You also might be able to tell because your control panel would probably have an option for adding MySQL databases.

Each different blog utility has different installation instructions; just follow the instructions they give you with the download in order to install and use it.

do you personally know of any free PHP/MySQL supporting hosts?

I used to use http://ashst.com until they closed free hosting; a popular one around here seems to be http://lifelesspeople.com, though I haven't used it myself.