“I’d Better Get Going” Means It’s Time for Me to Leave

“I’d better get going” is a natural way to end a visit, gathering or conversation. It means “it’s time for me to leave”. It sounds gentler than abruptly announcing “I’m leaving” because the speaker presents leaving as something the time or situation now calls for, rather than as impatience with the other person.

Here, ’d means had. Had better refers to a sensible action in a particular present or future situation; it is not a past perfect form. Do not say “I should better go”. “I should go” is possible, but more direct. For example: “It’s getting late. I’d better get going.” “No worries. Drive safe.” The expression is entirely natural in everyday Australian English, though it is not uniquely Australian.

https://dictionary.cambridge.org/dictionary/english/had-better
https://dictionary.cambridge.org/grammar/british-grammar/had-better