In order to disassemble one of these boxes, you may need: a flat blade screwdriver, a Philips screwdriver (usually #0 or #1 size), a Torx Security screwdriver (usually TR10 or TR15), a pair of needle nose or long nose pliers, and a pair of side cutters. (The exact tools required will vary between boxes.)
Note that the primary way to re-purpose one of these boxes is the removal of the hard drive (for use in a PC, laptop, or external hard drive enclosure), but there are also other components that can be salvaged and re-used.
If there are any other models that I have not covered, let me know or update this with the required details

Sky+, non HD, 80GB/160GB models: (contains 80GB/160GB 3.5 inch IDE hard drive)
https://www.youtube.com/watch?v=nqFkp2iYWn4
Sky+HD (Amstrad DRX890/DRX895) models, 250GB/500GB/1TB/2TB: (contains 3.5 inch SATA hard drive)
https://www.youtube.com/watch?v=bLAyVqNau7Y
Sky Q (latest model), 1TB/2TB models: (contains 1TB/2TB 2.5 inch SATA hard drive)
https://www.youtube.com/watch?v=cHs1u1i_F0o
Virgin Media V+HD, 80GB/160GB, HD model: (contains 80GB/160GB 3.5 inch IDE hard drive)
https://www.youtube.com/watch?v=JOZNpKvmeQE
Virgin Media (Samsung/Cisco) TiVo 500GB/1TB models: (contains 500GB/1TB 3.5 inch SATA hard drive)
https://www.youtube.com/watch?v=d5a9foqJdBc
Virgin Media (Arris DCX960) V6 TiVo, 1TB/2TB models: (contains 1TB/2TB 2.5 inch SATA hard drive)
https://www.youtube.com/watch?v=6isteKO4zxI