Well first off you have to have wamp or mamp running on your local computer, and if you don't know what they are, you probably don't want to do it.
You could install a second copy of wordpress in a subfolder of your host and create a Ned database, then export the current database and import it into the new one. this way if your site was your domain.com and the new wordpress install was in a folder called mytest, you would enter your domain.com/mytest to get to the test site.
You need to change the blog and home url's in the wp-options table but it is doable. then you could export the style from the test site and import it into the live site.