Visiting their Grave:

It is a traditional custom to visit the grave of your loved on their yahrzeit, unless that day is a festive Jewish holiday such as Sukkot, Shavuot, Passover, or on chol hamoed.[1] Also, one is not obligated to incur a great expense to visit the grave on the day of their yahrzeit.

What should you do when you visit the grave on the yahrzeit:

1.  Read Psalms: It is customary to recite Psalm 91 at the grave [2] and some add psalms 16, 17, 72, 104, and 130.  You may also want to recite the verses from Psalm 119 that begin with the letters of the Hebrew name of your loved one and from the word נשמה.  You may recite other prayers as well.

2.  “Malei Rachamim” prayer: It is also customary to recite the “malei rachamim” prayer in Hebrew or English.

3.  Learn Mishnayos: It is also a great mitzvah to learn Torah by the graveside.  Most people learn Mishna.  See more info on this here.(see above – incorporate above)

4.  Leaving the Grave: It is customary to leave a pebble or rock on the gravestone/monument.  Others have the custom to leave grass on the grave.

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[1] Pnei Baruch 39:21

[2] even within 4 amos of the grave