Since the output voltage range is twice as big as the input range, you need a voltage gain of 2. You will also need an amplifier ssupply of at least +- 5 volts. Assuming you find a rail to rail opamp so that you can get by with just +-5, you connect your input signal to the + input, and use two equal resistors in a divider between the output and a +5 reference voltage (the positive supply if it is accurate enough). The center of the divider goes to the - input.
When the input is at 0 volts, the output must go to - 5 volts in order for the divider to produce a matching 0 volts in the - input.
When the input is at +5 volts, the output goes to +5 volts and there is no voltage across the divider, so the - input is also at +5.