How to format hard drive and use time machine back up

my HD died, so i took the machine to the mac store, only to find it would cost me approx $300 to install new drive and OS, inc labor.

i knew this was a high price, so i opted to go to third party to install much better hybrid drive, which inc labor was cheaper.

so i have machne back but seen as they wanted a full $100 to install OS, its blank.

i just need help or how to on formatting and getting my time machine back up installed on new drive.

can anyone help with this?

many thanks!