Here's a conjugation table. The defining part is the -t (after consonants) or -tt (after vowels.)
Hungarian past tense is usually used when the English past tenses & sometimes when the English present perfect.
Ma meg nem ettem. = I haven't eaten today yet. (If I had eaten, it'd have been in the past.)
de! Három éve futok. = I've been running for three years. (I'm still running, so it's present.)
Reported speech is different from English. Present is used to say that it's the same time, while past is used to say that the thing reported happened earlier:
Azt mondta, hogy dolgozik (present). = She said she was working.
Azt mondta, hogy dolgozott (past). = She said she had been working.
The third person singular past tense indicative mood indefinite form (like dolgozott above) can be used as past adjectival participles:
az olvasott könyvek = the (widely) read books
Esperanto uses tenses the same way - not changing from direct speech to reported speech (so if she says "I am working" in the present tense then "She said that she was working" uses the present tense for "working" as well rather than changing it the way English does).