Here is a good start. There is a way of resolving the conflict between Network Manager and airmon-ng, so you can switch in and out of monitor mode without killing wpa_supplicant.

Open a new terminal window and type in or paste the following command:

Code:
gedit /etc/NetworkManager/NetworkManager.conf
Press enter. An editor window will open and it will look like this:

Code:
[main]
plugins=ifupdown,keyfile

[ifupdown]
managed=false
Add the following text to this file:

Code:
[keyfile]
unmanaged-devices=interface-name:wlan0mon;interface-name:wlan1mon;interface-name:wlan2mon;interface-name:wlan3mon
Now your NetworkManager.conf should look like this:

Code:
[main]
plugins=ifupdown,keyfile

[ifupdown]
managed=false

[keyfile]
unmanaged-devices=interface-name:wlan0mon;interface-name:wlan1mon;interface-name:wlan2mon;interface-name:wlan3mon
Save the file and close the editor. Changes take effect immediately. You can now turn on monitor mode using airmon-ng without having to kill the network manager. airmon-ng will still complain about these processes when you start it but they will no longer interfere with its operation.

Now as soon as you turn monitor mode off with airmon-ng stop wlanNmon, where N is the number of your wireless interface, 0, 1 and so on, the selected wireless interface will be back in station mode (you will be able to connect to networks and browse the internet normally from your Kali machine).