Assemble PIC connector from bits
First, let's use the right terminology.

The "black plastic bit" is referred to as the housing; the "little metal bits" are the contacts: in this case sockets. The ones in the picture, as SomeHardwareGuy inferred, are crimp type (as opposed to solder cup) contacts. They should be crimped with an appropriate crimping tool.

The tool in the photo is barely adequate and may do an acceptable job if the connector won't be used for anything critical. Do not use pliers! A good quality crimp requires very high pressure applied at the right point of the contact and pliers simply won't do that. A crimper recommended by most manufacturers is unfortunately, rather expensive. The cheapest good one I know of is the ProCrimper from TE Connectivity (formerly Tyco). It costs around $200 but does an amazing job and is well worth the money if you do a lot of crimped connections. This is a Molex page that explains what it takes to make a good crimp. The full document can be found here

There is a fairly low cost crimping tool being sold by a bunch of hobby outlets for anywhere from $20 to $40. I bought this one



from Hansen Hobbies. It does an acceptable job and is far superior to the one in the other answer, and costs a lot less than the ProCrimper shown here