Short answer: With the blur filter and a garbage matte.
Long answer: make a copy of your clip in the timeline, and place the copy above the original clip (i.e. in another video track). Apply a blur filter, and adjust the parameters to your liking. Then apply a garbage matte filter (four point or eight point, depending on the shape of the object you need to blur out) to that topmost clip.
If the object is moving, use keyframes to move the corner points of the garbage matte.
They can come in handy. You probably noticed, but there are two versions: one with four points and one with eight points. So depending on what type of shape you are trying to aproximate, use one or the other.
a quick note about Garbage Mattes.. always be sure you apply the matte and set all of your keyframes through the clip BEFORE you do any resizing/basic motion. It is an adventure in frustration to do otherwise, since your cursor will no longer point to the intuitive matte points (1-4 or 1-8). But these mattes are powerful tools!