There are several ways to access the developer console, however most of these are no longer valid as of Enemy Within. One way you can still use the console, however, is through the keybind method.
Find the DefaultInput file in the Enemy Within folder and add bindings under the
[Engine.PlayerInput] heading. If there isn't an
[Engine.PlayerInput] heading, then make one. Command bindings are written in the following manner:
.Binding(Name="< key >",Command="< Command 1 > | < Command2 > | < Etc. >")
It is suggested to that you add
ALT so that you don't accidentally use the console when you don't want to. To do this, just add
ALT=True to the binding.
Then, you can use your pre-specified console commands with their corresponding keybindings.