An asterism is a group of visible stars that is easily recognizable, such as Orion's belt. They can be useful to help orient yourself regarding the portion of the celestial sphere you are looking at, e.g., for celestial navigation or casual astronomy. An asterism may be a constellation, or the prominent stars of a constellation, but could also be a portion of a constellation or include parts of more than one. A telescopic asterism is one only viewable (or most easily discerned) using a telescope.
In ancient times a constellation was a "picture" perceived in the position of stars, adopted for use when discussing the stars for much the same reason as asterisms. This usage has been developed into a set of 88 (the modern constellations), each corresponding to a region of the celestial sphere, many of them based upon ancient constellations, having been standardized for use as part of the names of stars and other objects within the given region.
The term starfield refers to the portion of the sky around a star, basically, the likely field of view of a telescope when used to observe the star.