What dua can I make for someone who died?

You can make any sincere dua asking Allah to forgive, have mercy on and raise the rank of a Muslim who has died, such as "Allahummaghfir lahu warhamhu" (O Allah, forgive him and have mercy on him). Dua is one of the best gifts you can still give them, and it reaches them.

A short dua anyone can say

For a man: "Allahummaghfir lahu warhamhu." For a woman: "Allahummaghfir laha warhamha." It means "O Allah, forgive him/her and have mercy on him/her." You can also say it fully in English: "O Allah, forgive my mother, have mercy on her, make her grave wide and full of light, and gather us again in Jannah."

The funeral dua of the Prophet ﷺ

At a funeral prayer, the Prophet ﷺ was heard saying (Sahih Muslim 963):

"Allahummaghfir lahu warhamhu, wa 'afihi wa'fu 'anhu, wa akrim nuzulahu, wa wassi' mudkhalahu, waghsilhu bil-ma'i wath-thalji wal-barad, wa naqqihi minal-khataya kama naqqaytath-thawbal-abyada minad-danas."

"O Allah, forgive him and have mercy on him, keep him safe and pardon him, honour his arrival and make his grave spacious, wash him with water, snow and hail, and cleanse him of sins as a white garment is cleansed of dirt." You can use it any time, not only at the janazah.

A dua from the Quran

Allah praises believers who pray for those who came before them:

رَبَّنَا ٱغْفِرْ لَنَا وَلِإِخْوَٰنِنَا ٱلَّذِينَ سَبَقُونَا بِٱلْإِيمَـٰنِ "Our Lord, forgive us and our brothers who preceded us in faith." Quran 59:10

Your dua really helps them

The Prophet ﷺ said that when a person dies, their deeds end except for three: ongoing charity, beneficial knowledge, and a righteous child who prays for them (Sahih Muslim 1631). Children, friends and the wider community can all keep praying. When you pass or visit their grave, greet the believers there and ask Allah for their well-being, as the Prophet ﷺ taught (Sahih Muslim 975). See What do I say when I pass a graveyard?

Charity for them also helps. See Can I give charity on behalf of someone who died?

What about non-Muslim loved ones?

This is painful for many converts. Scholars agree that asking forgiveness for someone who died outside Islam isn't permitted (Quran 9:113), but you may still grieve, speak well of them, remember their kindness, and make dua for yourself and your living family. Leave their matter to Allah, the Most Just and Most Merciful. See How do I deal with grief as a Muslim?

Key points

"Allahummaghfir lahu warhamhu" is a short dua for a deceased Muslim.
The longer funeral dua is in Sahih Muslim 963 and can be said any time.
Dua from a righteous child continues to benefit the deceased (Sahih Muslim 1631).
For non-Muslim relatives, grieve and remember them kindly, and leave their matter to Allah.

Tip: Add one line for your loved one to the dua you make after each prayer. Five short duas a day, every day, add up to a huge gift over the years.