Hi and Welcome!
the cheapest way is to replace the BD-ROM by a BD writer.
If you insist on having the drive externally, then you need an external 5,25" enclosure that supports Sata drives. The external interface depends on what you have. USB2.0 HiSpeed is most common, but I’d personally prefer eSata if the computer has such a port.
P.S.: It’s better to have a new thread about this (thread hijacking is impolite), so I moved this stuff to a new one.