I've heard of and many years back did do a motherboard replacement of a desktop computer. But a laptop computer requires such critical packaging control that I'm not sure if a novice can replace a laptop computer motherboard. But if it is at all possible, you must obtain the precise motherboard that fits your package model. By doing it yourself you will have no warranty or assurance that your actual problem has been fixed. If replacing with a new system is out of the question, I would pursue a local computer store or online facility to do your repair. But I'm afraid the short answer to your question is if you have to ask how, don't do it.
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There are 10 types of people. People who understand binary and those who don't.
IF you are detail oriented, and take your time, it's not too difficult to do. First, I'm assuming your replacement board is the same motherboard as what is currently in the laptop. Getting the laptop apart (without damage) is sometimes the most difficult part. There is a combination of screws and snap-fit parts that will need to be removed, and there are delicate cable assemblies that will need to be removed in the process. As screws and assemblies are removed, I try to set them out in layout that is similar to the location where they belong in the laptop, this helps when it comes time to reassemble. I take pictures during the disassembly, to help with wire-harness routings, etc. DO NOT FORCE anything, they didn't use a hammer to build the laptop, you shouldn't need one to take it apart!
If you post the model of your laptop, I may be able to offer more specific instruction.