From a quick Google it looks like this should be fairly straightforward. Sometimes the problem is not actually with the socket itself but that a piece of plastic holding it in place is broken, so that when you push the power connector in it simply pushes the socket further into the case rather than fully engaging with it. In such cases you have to use a bit of ingenuity. Epoxy glue can come in handy.
As for tools you just need screwdrivers, but the iFixit jimmy is very helpful for releasing case clips. If the case resists then take to heart my motto: there's always one more screw!
Talking of screws, stick them to a piece of paper with blu-tac and write against each blob where they came from.
The iFixit spudger https://eustore.ifixit.com/en/Tools/Prying-Opening/Spudger.html is also pretty useful for releasing ribbon cables from their sockets. Take care with these - if you break the release bar then you've pretty much had it.
Don't remove the heatsink unbless you absolutely have to as you'll then need to replace the heatsink paste, and if you don't apply it correctly your processor will overheat and shut down.