One of the best ways to pay off our Pitru roon is perform shraddha. This is a special prayer that is performed on the death anniversary of the person. There are many times where we may not know the death date of a person- particularly as we think of several prior generations ago- for e.g. you may not know the death date of your great grandfather. In all such instances, you can perform these special prayers during the Pitru Paksha. Please refer to our post on the Significance of Pitru Paksha for more details.
How do we perform these prayers?? Personally, what I have found immensely helpful is to simply offer food and water to our ancestors with usual prayers. Light a special lamp (diya) and an incense to specially offer them thanks and express gratitude- in plain language.