You will need to be connected to the internet to update your system. It is always advisable to make a backup of your image first (and at a minimum, make a copy of your important files).
You can check your current version of firmware with the uname -a command, as follows:
Linux raspberrypi 4.4.9-v7+ #884 SMP Fri May 6 17:28:59 BST 2016 armv7l GNU/Linux
The GPU firmware can be checked using the /opt/vc/bin/vcgencmd version command, as follows:
May 6 2016 13:53:23 Copyright (c) 2012 Broadcom version 0cc642d53eab041e67c8c373d989fef5847448f8 (clean) (release)
This is important if you are using an older version of firmware (pre-November 2012) on a newer board, since the original Model B board was only 254 MB RAM. Upgrading allows ...