Relative clause
When you want to add additional information about a noun in a sentence, you describe it using a relative clause. In The woman who studied abroad talked, the relative clause who studied abroad is a description of the woman.
In Tamil, there is no such a construct. Instead you make the whole description an adjective of the noun and place it like any other adjective in front of the noun.
This is possible by using the -அ「-a」 suffix after the present tense and past tense verb stems and -உம்「-um」 for future tense. Apart from the different suffix, you keep the entire sentence structure and place it as a whole in front of the noun.
If you now combine these, you get
which is correctly translated into
The woman who studied abroad talkedIt is important to note that you use the right tense when building the participle to ensure that the right meaning for the relative clause is created.
வெளி நாட்டில் படித்த「veḷi nāṭṭil paṭitta」 describes someone studied abroad (in the past) while வெளி நாட்டில் படிக்கிற「veḷi nāṭṭil paṭikkiṟa」 is talking about someone who studies abroad (now).
The future participle is less used in spoken language.
செய்「cey」 → செய்யும்「ceyyum」 — to do
The negative version of this participle is created by using the suffix -ஆத்「-āt」 in front of the -அ「-a」. There is no differentiation between tenses here, you add this suffix to the verbs root.
வெளி நாட்டில் படித்த「veḷi nāṭṭil paṭitta」becomes
வெளி நாட்டில் படிக்காத「veḷi nāṭṭil paṭikkāta」in the negative (படி「paṭi」 + க்「k」 + ஆத்「āt」 + அ「a」).