Without getting into the expensive hardware...two machines sharing one drive is the easiest. You simply have the drive connected to one machine, however the drive connects (Thunderbolt, eSATA, Fibre)...and then you network that one machine to another via Ethernet...and then share that drive. Then both machines can access it.
Now, this must be a FAST connection...eSATA, Thunderbolt or Fiber, because two machines are going to try to stream video from it...so it must be capable of at least 6-10 streams of video.
For more than two...now you get into the "SERVER" territory. A server connected to a RAID array, and then to an ethernet switcher that then connects to the multiple machines. The more machines you want to access the footage, the faster the RAID is going to have to be...again, more streams of video.
The first option you can do yourself simply. The second solution...don't attempt this yourself unless you are an IT expert. Hire someone to build it...or rent it.
Sorry, you cannot simply connect 4 computers to a single drive. It's not that easy.