The fixes
Full stop, semicolon, comma + coordinating conjunction (for, and, nor, but, or, yet, so), or subordinate one clause (Because the store was closed, we went home).
The "however" trap
It rained, however we went. is a splice. "However" is an adverb, not a joining word: It rained; however, we went.
Are they ever acceptable?
In fiction and informal writing, very short, parallel clauses are sometimes spliced for rhythm: I came, I saw, I conquered. In essays and professional writing, fix them.
Frequently asked
What is the difference between a comma splice and a run-on?
A comma splice is one kind of run-on: the one with a comma at the join.