Well, first step is to identify your chipset. You can do that with for example CPU-Z. Then, you should research which is the fastest processor which is supported by that chipset. Good starting point for Intel is http://ark.intel.com/ and for AMD is http://products.amd.com/en-us/NotebookCPUResult.aspx
Next step is to determine how to access your own processor and to make sure that the processor you have can be easily removed. Some laptops have sockets, while other have soldered processors. It is almost impossible to remove the soldered processor, so if you have one, then you're reached a bad end and there nothing you can do.
Next next is to see how much thermal power does your processor radiate. From the list of compatible processors, remove any which have higher power.
Now you have a starting point. Next step is to do some research on the Internet and try to find anyone who installed that processor in the same laptop or in a similar laptop or in a laptop with same chipset. It would also be a nice idea to find laptops which ship with that processor and see hat are their specifications.
After that the only remaining thing is to actually get the processor. By now you should be able to determine if it will work or not. Picking the processor itself is a bit risk, unless you can return it, because there's always chance that it will not work. If it works, congratulations. If it doesn't then please accept my condolences.