Know and Understand can take past, present and future forms in Tamil.
Both verbs also use the subject in the dative case. So instead of "I know", it translates a little more like, "it is known to me."
Past: Knew: தெரிந்தது
Present: Know: தெரிகிறது
Future: Will know: தெரியும்
Pres/Past Negative: Did not/do not know: தெரியவில்லை
Future Negative: Will not know: தெரியாது
Past: Understood: புரிந்தது
Present: Understand: புரிகிறது
Future: Will Understand: புரியும்
Pres/Past Negative: Did not/do not understand: புரியவில்லை
Future Negative: Will not understand: புரியாது
Remember that habitual actions take the future tense (even though they take present tense in English) so you may end up using the future forms of these verbs more often, because it does not just mean "I will know" or "I will understand" but also to inform of a general understanding as well.