One way is to set up key frames to follow the target you want to blur out. You may or may not need to vary the size of the mask depending if the video is zooming in and out which of course would change the target size besides any lateral movement. How much work is involved depends on how long the event you're working on is, how fussy you're going to be like blocking out just the target or an area near the target. It is easier to do than it sounds.

Do as GG suggested. Now while watching the preview window adjust the size of the circular area of the cookie cutter mask to just cover the target area of your subject in the first frame. You move the mask around by dragging the little square inside the work window of the filter. You resize the mask moving the sliders. Play a second or two of the video and see how much your subject moves and how well the mask is tracking. If there is a lot of movement you'll need to insert key frames more often. That's basically all that's to it. Once you get the hang of it, you can gain much finer control if you advance the video one frame at a time using the arrow keys by holding down the Atl key at the same time. Be sure you click on the timeline first otherwise you'll be adjusting the mask and not moving the timeline.

Another cool trick done easily in Vegas Video.