There isn't a whole lot that is likely to trip you up. Basically you either do the one-click install to the subdomain, or extract a downloaded archive as usual. Then you'll get routed to the install directory as always when you first visit the site.
Most everything about the install location will be automatically entered, but just insure that you're using the subdomain whenever asked for the site url.
You'll be able to connect to MySQL with the typical database credentials. Just make sure you have a database for the subdomain seperate from any other Joomla installs you might have previously used. I know there is support for multi-site stuff on a single database, but I avoid that for the most part.