Do you see how (in S4) the gold print is arranged like 2 combs pushed together? One comb is one contact, the other comb is another contact. The soft button is coated with a conductive film, and when pushed it connects the two combs. This IS a switch. This type of switch has a higher resistance than most switches, and can also handle only much lower currents. You can consider them ON or OFF, 0 ohms or infinite ohms, but whatever you are turning on/off cannot draw much current. (like less than 10 mA)
It is used just like any single pole single throw switch (i.e., common light switch). One contact is connected to ground OR power, the other is connected to the device to be turned on or off, the other side of the device goes to the opposite Power OR ground. In this case, the controlled device is an arduino pin, and that pin should be an input. (pinMode (INPUT) or, better yet, (pinMode(INPUT_PULLUP).
In the latter case of input pullup, you connect one side of the switch to ground, and the other side to your pin. The pin normally sits there in a high state, and when you push the button (or connect the 2 contacts) it drops to a low state. In other code, you then compare what state the switch is in, and do the action you desire for the state the switch is in.
In (DS2), there is a LED as well as a switch. (Probably intended to light up a translucent button.) You do not have to light the LED to make the switch work, the LED and the switch are separate components on the board. If you want to light the LED, be sure there is a current limiting resistor in the circuit. (There is not one shown in your picture, but there is likely to be one on that board. You must be sure.)
Is this a section of a remote control? Can you tell us more about it? Model? MFG.? Original use?