First, start a server with stats enabled. Add ?LogGameplayEvents to the URL when you start the server. So, your final target will look something like
UDKGame.exe server AOCLTS-Arena3_p?dedicated=true?Adminpassword=testjpassword?LogGameplayEvents
Stats show up in UDKGame\Stats\...
The box at the top of the window is the file list. The drop-down menus above let you set filters for the files; leave them at "All time" and "Any" to show all the stats gathered for the level. You can ctrl or shift-click the files to select more than one file at once to aggregate the data over multiple sessions, which is very useful for heatmap generation; if you do so, you can no longer change the time range, it spans the entire length of all included game sessions.
Underneath the file list, you'll see a bunch of tabs; there's one for each visualizer. You can also switch tabs to different visualizers by clicking the drop-down menu (so you can have a bunch of tabs open with the same visualizer, but with different options).
Click "Enabled" at the top-right of a tab to enable a visualizer. Some visualizers (like Heatmaps) have options; click the Options button to access these.
The first of the three boxes underneath there lets you pick the specific stat(s) to visualize. The second lets you pick a team to visualize (* not working in Chivalry at the moment). The third lets you pick a specific player or players (shift or ctrl-click).
Finally, make note of the Time Range at the bottom. The spinbox at the left of the slider lets you set the first frame to see, and the right side sets the last; if you just type in 0 in the first and a very large number in the last, you can stretch the range out to cover the whole game session. Otherwise, you can drag the timerange slider around to see how things unfolded during the session, and you can use the Play button to have it automatically animate for you. If the slider and spin boxes are greyed out because you have more than one file loaded, ignore their values; again, when you have more than one file loaded, the timespan covers everything.
Heatmap options
(Note: Heatmaps only show in orthogonal (top view) viewports!)