Past tense in Sindarin covers almost all forms of past tense in English. I watched; I have watched; I have been watching - these are all translated the same way.
This tense is formed by adding a suffix to the verb, so it is referred to as the "weak past tense." Its meaning is exactly the same as the strong past tense, these are just for different classes of verbs.
When conjugating A-verbs, you must take into account whether the verb is intransitive or transitive. Transitive verbs are verbs that take a direct object; intransitive verbs don't take direct object.
The transitive past tense suffix of the A-verb is -nt.
Lasta- → Lastant it heard
Dolla- → Dollant it concealed
Minna- → Minnant it entered
Dringa- → Dringant it hammered
To make the forms for the other pronouns, you add an -e to the end of the past tense verb, which turns the nt into nn, then add the pronoun suffix. In the case of roots that end in -nna, to avoid -nnanne- it is simplified down to -nne-.
Lastant → Lastannen I heard
Dollant → Dollanneg you concealed
Minnant → Minnedh y'all entered
Dringant → Dringanner they hammered
The intransitive/impersonal past tense suffix is -s or -st. There is no difference in meaning between them; they can be used interchangeably.
Lasta- → Lastas it listened
Delia- → Deliast it hid
Muda- → Mudas it labored
Brona- → Bronast it survived
To make the other pronouns' forms, add an -e, and it will make the -s or -st into an -ss-. Then add the pronoun suffix.
Lastas → Lastassef we, not you, listened
Deliast → Deliasseg you hid
Mudas → Mudassedh y'all labored
Bronast → Bronasser they survived
Notice how the -s(t) suffix can be used to change a verb's meaning slightly? With this, you can make a verb intransitive. So, if you have a word that has a very similar meaning in the transitive like "to hear," you can put it into its intransitive version: "to listen." Keep in mind that there are some verbs that this just won't work on, like "to come." There's no way you can make that transitive.
Long ago, when the languages were still Common Eldarin, the verb-augmenting suffix -ta was a separate morpheme. In Sindarin, -ta has long since been absorbed into the verbs. The only times that we see evidence of it having been there is in the past tense and (rarely) in gerunds. The -ta will be dropped from the verb root and these words will be treated like I-verbs instead of A-verbs. Therefore, they'll be covered in I-verb section instead of the A-verb section.
These verbs are listed with the portion dropped for the past tense in (parentheses). These aren't all of the TA-verbs, just the ones that we have evidence to suggest would lose the TA and act like I-verbs.