Didn't you download the files from your previous provider? including a DB backup?
If so, use those file's to set up your forum at your new service provider.
If not, in most cases all that you need to do is copy the style files into your templates directory and then choose that as the default style in the configuration page in the administration section. In more complicated styles there will likely be instructions to install it. In either case, you'll likely need at least some sort of FTP client (FileZilla
is a good one) and FTP access to your server which you can get from your hosting provider.
If you need help with this, send me a Private Message
and I can at least recommend someone who can help.