You will find plenty of detail about the planning process on the Wandsworth council website. If you are considering making a planning application yourself. the place to go is here - for application forms, details of requirements and restrictions.
If you are concerned about a planning application in your neighbourhood, you can see full details, and make a comment, or lodge an objection here. The process is speeded up a little if you know the reference number of the application, but there are other ways in which you can locate the details of the application.
Every week Wandsworth Council publishes a list all applications advertised in the preceding seven days. The full list is available here. If you are likely to be affected by a development near you, you may receive notice of an application, but as a safeguard it is useful to register to receive details of any planning applications in your area. You can do that via this page.
We must stress that the Battersea Society cannot provide specific planning advice and you should always seek professional assistance with any planning issues.