They need to write to the planning officer (whose name should be on the letter sent to them by the council) saying they object to the application and giving the reasons why.
In this case it sounds like the main reasons would be that it would result in significant loss of light/overshadowing to their rear rooms and rear garden and would create an oppressive/overbearing environment when viewed from these rooms and garden. THis would result in significant detriment to their residential amenities.
They should expand on these objections, setting out things like you've put in your post, e.g. the extension is to the south so it will block light, the size of the house now and if extended, how deep (long) their garden is, how close it will be to their garden/rear windows, what rooms their rear windows serve (if they are bedrooms, living room, kitchen, dining room etc, then they are 'habitable' rooms and generally have more protection than if the rear rooms are utility, bathroom, landing, hall, ensuite etc, 'non-habitable rooms') etc.
If there are no new windows that will overlook them then it would be difficult to object on the grounds of overlooking/loss of privacy but they could ask for a condition to be imposed preventing any new windows being inserted in the elevation facing their garden if permission is granted.
If they don't think the design fits in with the scale and design of the existing house or streetscene they could also object on this basis.
They should ask for the planning officer to visit their property to view how the extension would look from their rear windows/garden. If a proposal is going to impact on nearby dwellings then it is good practice for the planning officer to have a look at the site from the potentially affected property and take photos.
They could also speak to their local councillor (not a parish councillor but their district/borough councillor) setting out their concerns as well.
Their letter will become a public document and so will go on the planning file so anyone (including the people who have made the application) could read it or ask who, if anyone, has objected. Not trying to put them off writing a letter but just making you aware of this as not everyone realises.
Whether it will be refused or approved really depends on the circumstances of the site and its surroundings and I can't advise on that.
Hope this helps.