For the ground wire you make a chain..... Connect the ground wire to your first buttons ground connection, then connect a wire from that connection to your second buttons ground connection, connect a third wire fron the second buttons ground to the third buttons ground..... and so on!
The other four wires, connect the button1 wire marked on the manual, to the NO (Normally Open) connection on button1, connect the button2 wire marked on the manual, to the NO (Normally Open) connection on button2 etc etc until you have all the buttons wired.
You don't want any of those white connectors. They're mostly used in fruit machine gamblers and you need special tooling to fit them, they're also not available on the high street.... You want some "female crimp connectors" and a crimping tool to attach the wires to them. You can get those from most automotive parts stores, just make sure to buy a size that will be a good push fit onto the tags on your buttons. Take a button with you to the store and try them.
Best Regards,
Julian (Fozzy The Bear)