The central plot of the film revolves around the titular spider invasion, which occurs when what appears to be a meteorite crashes down in rural Wisconsin, and spawns spiders of varying sizes.
Subplots include:

Dan Kester and his hate/hate relationship with his wife, Ev
Dan's adulterous affair with local barmaid Helga
Dave Perkins' attempts to make out with Ev's underaged sister Terry
A fundamentalist preacher leading a revival meeting
Drs. Vance and Langer getting involved in somewhat of a romance (all the more notable as the two lead actors were also in their early-mid 50s when the movie was made)
The eventual panic that results when the townspeople are confronted with the spider
The invasion is deduced (with various scientific-sounding language) to be the result of some sort of interdimensional gateway, and is ultimately thwarted when Drs. Vance and Langer manage to close off the gateway, draining the spiders of their energy and causing them to melt into puddles of disgusting sludge.
Who is Ev's sister?
Terry