The connector type used on the main board of the µBITx and the Raduino are of type KF2510. These were developed by MOLEX and are of the polarised and locking type with 0.1″ spacing between pins. They are commonly available everywhere. In the US they are available from Tayda and Mouser. In Australia and New Zealand they are stocked by Jaycar. If you have time for delivery they can be obtained cheaply on AliExpress and Ebay websites, including in sets in a plastic storage box.
The KF2510 comes with both straight pins (for connectors to a board) and with 90 degree pins. The 16 pin connector between the Raduino and the main circuit board uses the 90 degree type on the Raduino end, and straight female socket on the main board.
Connecting wires to the female connectors is straight forward. Line up a section of wire (stripped back by around 1/4″) and use needle nose pliers to crimp the bottom-most crimp section first, and then the top one. Most of us apply a dab or solder between the crimps to secure the wire firmly to the female pin.
The female pins just push in, but must be oriented correctly in order to be held firmly in the socket. If they come straight out you are putting them in backwards. The female pins are easily removed by pressing on the back of the metal pin with a flat-head screwdriver by reaching through the little window and at the same time pulling on the wire. Rather than curling up your spare wire connectors, it is better to pull them out of their socket for storage in the junk box. They can be reinserted when you want to use the connection again later.