First of all, remember static electricity is your enemy, keep this in mind while you are messing around inside your laptop, making contact with bare metal is better than nothing, but consider a grounding strap while you are handling the insides of your computer.
Dis-assembly isn't the hard part or even the tricky part... (if you have decent memory that is, if you forget things easily, then taking pictures often will help) Soldering anywhere on/near any electronic board without frying said board and getting it to work in the end is the hard tricky part... Before doing this, look for replacement motherboard or whatever power port is attached to, never know might save yourself the trouble by buying $100 board... (or you might end up having to get it if you fry your motherboard)
If wires are soldered onto power port (with other end soldered to motherboard) and it is screwed to motherboard (not soldered directly to board) then remove it, use soldering gun to disconnect wires from it (taking note of each wires location, make yourself a map and showing the pins of the power port and saying which wire goes where, or label each wire top/left, top/right, bottom/left etc. being sure to note the orientation of the power port). On new power port, carefully solder wires on the correct pin, making sure not to over heat wires and making sure mother board and other electronics are protected at all times. If you aren't good at soldering, think very carefully before you attempt this, you can ruin your motherboard with one simple slip...
Another alternative if you have enough space is cutting wires off, leaving yourself enough room to splice them, solder wire onto new power port, then splice wires back together using heat shrink tubing to insulate wires (being really careful where you aim your heat!) and then finally screwing power port back down on motherboard.