Cutting scene results in choppy transition
The two most common approaches, if you don't have B-roll coverage, is either a dissolve (usually a cross-dissolve) or a fade-out/fade-in (usually dip-to-black).  Garish effects (essentially all the others offered in a typical NLE) can also be used (but are usually avoided).

IF the clip you are cutting out means joining what looks like a single take (with a discontinuity in the middle), the dip is your friend.  If the clip you are cutting out takes you from one scene to another, the cross dissolve can also work.  A series of cross-dissolves can work to show the passage of time (where the camera stays fixed and the subject is seen doing on thing, fading into doing another, etc.).