Introduction
I bought a kit to fix this component. The kit contained the headphone jack itself, a Phillips #00 Screwdriver and an Opening Tool.
I made do with just the above tools, but my instructions use the ideal tools should you have them.
I also replaced the rear camera at the same time, by following the excellent guide for that component.
Tools
Parts
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Insert a SIM card eject tool or a paper clip into the hole next to the SIM card slot, which is located just under the power button. Do not force the paper clip if it is too thick; instead use the head of a sewing needle.
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Push the tool into the hole until you see the card pop out.
 
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Gently remove the SIM card with your fingers, or a pair of tweezers if the SIM holder does not fully eject.
 
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Remove the six 4.0 mm Phillips #00 screws that secure the midframe to the phone.
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To replace the LCD screen and digitizer, remove the additional four 4.0mm daughterboard cover screws with the same screwdriver. You may have to pierce through clear adhesive material to remove them.
 
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Use the flat end of a spudger to disconnect the daughterboard ribbon cable and pull it away from the battery.
 
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Use a plastic opening tool to pry the battery out of its housing.
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If replacing the battery, bag the old battery up and recycle responsibly at a suitable location.
 
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Use the flat end of a spudger to disconnect the ribbon cable that connects rear-facing camera to the motherboard.
 
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Use a spudger or tweezers to pull the headphone jack upward and out of the phone.
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Place the new headphone jack by orienting it like the old one and pressing it gently down into the phone.
 
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To reassemble your device, follow these instructions in reverse order.