The reason you might not get very many responses is that there are so many things to think about that one can end up writing an essay. You could do some research and ask SPECIFIC questions when you get stuck and not just request somebody to guide you through every point and eventuality here. We know not whether you know how to cut pipework, or switch the hot water off, or operate a drill or whether you have a tap spanner or know what PTFE tape is etc. In a nutshell:
- Turn off hot water.
- Turn off cold water.
Even the above two issues can be easy or hard. Can you do this? If not then we have to start discussing what sort of system you have e.g. combi boiler or regular boiler and cylinder etc. as they require different methods.
- Remove basin from wall...
What tools do you have? You will likely need a tap spanner. Will the new taps line up exactly? If not then other questions and answers need looking at.
- Replace new basin and taps.
Requires lots of effort to tell you how to do this whole job. Even fixing it to the wall can result in complications: what's the wall made of/does it need strengthening/use X fittings etc.
Although it seems an easy job - if you have zero plumbing knowledge then prepare to do some research, keep asking questions (targetted questions), buy a couple of new tools and spend a fair bit of time doing the job. It is satisfying when completed - if you are that way inclined.
Can end up cheaper calling a plumber in (unless down South