Unpack the WikklyText package under either modules/ or sites/all/modules (you should end up with a directory modules/wikkly_fmt, or sites/all/modules/wikkly_fmt).
Go to Admin|Site Building|Modules and enable the WikklyFormat module.
Go to Admin|Site Configuration|Input Formats
Click Add Input Format
Select WikklyText, Full Mode or WikklyText, Restricted Mode (but not both at the same time).
Name the format something like WikklyText, Full or WikklyText, Restricted (as a reminder to yourself).
Select which Roles may use it
CAUTION
Full Mode is for trusted users only. Full Mode allows the user to execute arbitrary code (by design), and should only be given to people you would trust to access the PHP code input format (for example).
Restricted Mode is for all other users. It can do 95% of what you would normally want to do anyways, without allowing arbitrary code execution or calling unsafe macros.
WARNING: As of this writing, Restricted Mode has had very limited testing "in the wild". Is is believed to be safe, but to be cautious, you might not want to allow untrusted users to access even Restricted Mode until it has been more widely tested.
There is no need to add additional filters to the input chain when using a Wikkly format. Adding filters in Full Mode will remove necessary document structure. You can add filters in Restricted Mode if you prefer, but WikklyText is designed to be safe on its own.
When creating content, select the desired WikklyText filter under Input Format as shown below: