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 the firmware to make use of the extra memory if available.

The free -h command will detail the RAM available to the main processor (the total RAM is split between the GPU and ARM cores) and will give the following output:

                 total       used       free     shared    buffers     cached
    Mem:          925M       224M       701M       7.1M        14M       123M
    -/+ buffers/cache:        86M       839M
    Swap:          99M         0B        99M
  

You can then recheck the preceding output following a reboot to confirm that they have been updated (although they may have already been the latest).