It sounds like someone at BT has sent a replacement box, rather than a full kit. It should have come with a remote control, a set of manuals and all the leads you need.
There's actually no such thing as a "BT Sport" box. It will be either a BT Vision box (more likely) or a YouView box (says "YouView" on the front). Both are Freeview receivers, though the BT Vision box can't do Freeview HD.
It connects up to the aerial and the TV just like any other Freeview box does. It also needs to connect to the broadband by an ethernet cable.
Since it sounds like BT have messed up, try contacting them using one of the methods given in the Contact Us section of the web site. There's an icon for it at the top of this forum page. Make sure you talk to the dedicated BT Vision help line.
If the manual is missing it can be found on-line via this page.
Click on the top left link on the page if the box is a BT Vision one.
Click on the bottom link on the page if the box is a BT Youview one.
Is your neighbour on normal BT Broadband or Infinity?
If he is on normal BT Broadband he should have been sent a BT Vision box and a viewing card.
If he is on Infinity Broadband then he should have been sent a BT Youview box. (no card required) (assuming he didn't also order Sky Sports which are not available on BT Youview)
As Ectophile said, BT may have thought they were sending out just a replacement box, and hence assumed he already had the leads, remote and manual. BT's mistake and they should resolve it by either sending the missing items or sending a whole new complete package.
The BTTV box doesn't have to replace any existing Freeview box, though it is designed to provide full Freeview PVR functionality. Your neighbour could have both boxes connected to the TV using two HDMI ports or one HDMI and one SCART (doesn't support HD) port if he so wished. The sports channels will only be available on the BTTV box. The BTTV box does also have to be connected to the BTHomeHub.