此 + [noun]
在此 / 从此 / 此时 / 此次 + [verb phrase]
此 means "this". It is the written counterpart of 这, and it sits straight before a noun, with no measure word. You'll see it on signs, in notices and in news.
Most of the time 此 comes inside a short fixed pair. Each one has an everyday equivalent with 这.
从此 marks a point in a story and says what held true from then on. Its everyday form is 从那以后.
In speech, and wherever you would need a measure word, use 这.
此 also sits inside 因此 "therefore", 如此 "so, like this" and 此外 "besides". Those are separate words with their own points.