Hi and welcome to LinuxQuestions!
Sincerely I don't know at which level you need a step by step guide to remove a directory, therefore I assume you ask for a command line solution, having no experience of working with it. You have to open a terminal, digit the following command line
rm -ir ~/.gconf/system/networking
and press enter. This will remove the entire directory, but will ask you for confirmation about deleting every single file inside it (just to be sure you don't damage your system or inadvertently remove some other file). Press y to answer yes, n to answer no.
I assume you know what you're doing. The ~/.gconf/system/networking directory contains the configuration of the network devices on a per-user basis. If you delete it the Network Manager will re-create the directory at a later use. Hope this helps.
An aside note: when asking a question, it would be useful to specify on which system (linux distribution) you are running on, if you're using a Desktop manager, which Desktop manager and so on. The more details you provide, the more effective will be the answer.