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.
- Martin