Three short rules. No boring theory — just listen, notice, remember.
Use A before a consonant sound. Use AN before a vowel sound. The sound matters — not the spelling.
university starts with a "y" sound — that's a consonant. hour starts with a vowel sound, even without "h"
The first time you mention something, it's new — use a/an. After that, everyone knows which one you mean — use the.
Plural nouns in general, uncountable things, meals, languages, and most names and countries — no article needed.
Quick test: can you say "this exact one"? Use the. Can you say "just any one"? Use a/an. Talking in general? Use nothing.