Be sure to read the 'Wireless' page for general information before you read this page.
Unlike the standard Lego EV3 operating system which is only compatible with a specific model of WiFi dongle (Netgear WNA1100, available from Amazon), the EV3dev software should be compatible with many different kinds of WiFi dongle, including dongles that are much more compact than the Netgear dongle. I myself use the Netgear dongle with EV3dev but that dongle is large and therefore to avoid having the dongle sticking out horizontally from the robot I use a cheap right-angle adaptor (FR, UK) so that the dongle is vertical.
There are two ways to set up WiFi on the EV3: using the Brickman interface on the EV3 or using the command line.
Set up WiFi using the Brickman interface
It's possible to set up the WiFi connection via the Brickman User Interface on the EV3 but currently ev3dev.org offers no instructions or help for this. I set up my connection this way with no difficulty so you will probably manage it too - I suggest you try this method first because the instructions for the command line method look more complicated. According to page 11 of this PDF document the steps are as follows (I added the 'connect automatically' step):
The above steps do not include the setting up of a static IP address for the EV3, something we are advised to do on ev3dev.org when setting up a USB connection. I will make it clear later whether this step should also be done for WiFi, once I'm sure...
Set up WiFi using the command line
To be able to use the command line you must have another way to connect to your robot first before being able to use WiFi. If you have followed my instructions you will have already set up a USB connection to the EV3 and (on Windows) you are probably using PuTTY or MobaXTerm to communicate with the EV3 from the PC using the command line. Follow the instructions HERE to set up the WiFi connection using the command line. this method has the advantage that it makes it much easier to enter the passphrase.
Whichever method you use to set up the WiFi connection, you should only have to set up the WiFi connection once - the connection should be established automatically in future sessions.