Once your neighbour applies for planning permission a "Neighbour Notification" letter should be sent to all properties which border with the applicants property. You will then have 14 or 21 days to view the plans at the council offices and place your objections. We live on a narrow private lane and all of the houses here have huge gardens, we have had three of these residents apply recently to build large 5 bedroomed detached properties on their gardens. Once all the other residents got together and put across their objections, we know that 2 out of the 3 have been given a knockback.
You are best to oject on every ground possible. Examples are, overcrowding, overshadowing, noise levels when extension getting build, privacy rights ie will any windows look onto your property, traffic problems when construction under way ie will the emergency services be able to access your property during construction work (seemingly always a good one), parking problems due to construction work and afterwards especially since they are doing away with the garage, appearance of extension in keeping with the rest of the street, will the materials for the new extension eg roof tiles etc match what is already there or will it be an eyesore, impact on natural environment ie will the area be too built up, how close to your own borders will the extension be (there is a legal limit), safety for children walking to school etc highlight the fact that diggers, lorries etc could cause huge safety problems for little kids. Thats all I can think of just now.
We actually involved our local Councillor for her points of view.
Once you note all your objections the Council then have an obligation as to let you know what the final outcome will be. I live in Scotland and what I have written is applicable to Scottish law, but I presume the English system is the same.
Best thing to do is go the planning office and ask to see the plans and ask the planner there for advice. They are usually really helpful. If any of your other neighbours feel the same as you, it is best you all write similar letters, preferably one from the husband and a separate one for the wife, as the more letters they get objecting the better.
Good Luck.