First and foremost you need to disassemble the laptop and remove the motherboard. Locate the DC jack on the motherboard, typically speaking, it is an almost square component with a metal casing located at the back of the board in relation to where it was in the laptop. Using a soldering iron set to around 800° F, heat and remove the solder holding the DC jack to the board. Removal of the solder is best achieved by using a desoldering pump. You may need to turn the motherboard over to completely loosen and remove the solder. You may be tempted to pull the component if the solder is almost off; do not do this! You run the risk of damaging the motherboard permanently.
After removing the component, take a small amount of 99% pure isopropyl alcohol and apply it to an old tooth brush and gently remove the solder film, also called flux; this creates a clean surface for the new DC jack to be connected. Be sure the soldering iron is cleaned after the disassembly process to prevent dirt and debris from becoming attached to the contacts. Take the replacement DC jack and apply a small amount of solder to each contact; then apply a fresh bit of solder to the leads on the motherboard prior to attaching the component.
It is important that both sides of the motherboard have solder applied to them to ensure the best possible contact with the DC jack component. At this point you are ready to connect the jack to the motherboard. Place a small box or piece of wood under the DC jack and place the motherboard on top. Simply apply fresh solder to each of the leads and the repair is complete. Should you need to correct an incorrect solder simply use the iron and desoldering pump to remove and reapply. Finish by reinserting the motherboard into the laptop.