Good grammar is the sign of either a good primary education or a heavy reader. With enough reading, the reader will intuitively get transitive vs intransitive right without even knowing those terms. (The use of the subjunctive works similarly.)
I remember the difference by thinking that a transitive verb transfers the verb's force to something. Intransitives just exist. "I hit the ball" vs. "I exist."
Lousy grammar bugs me and it bugs Ann Althouse: "The worst thing about Rubio's repeated line isn't that he repeated it, but that he thinks 'dispel' is an intransitive verb..."
Actually, I think Rubio meant to say "dispense," and misspoke.