Go ahead with your prayer, and after completing it, you need to perform two prostrations for inadvertence (sajdatā al-sahw), for adding salam.
The method of performing sajdatā al-sahw is that immediately after the salām of the prayer, you must make the intention of sajdatā al-sahw and place his forehead, based on obligatory precaution, on something on which performing sajdah is permitted. The recommended precaution is to say dhikr in the sajdah, and it is better that you says:
bismil lāhi wa billāhi, assalāmu ʿalayka ayyuhan nabiyyu wa raḥmatul lāhi wa barakātuh
(In the name of Allah and by Allah. Peace be upon you O Prophet, and Allah’s mercy and His blessings (be upon you too).
Then, you must sit up and go into sajdah again, and say the dhikr mentioned above. [you must then sit] and say tashahhud, after which you must say:
assalāmu ʿalaykum
Peace be upon you all.
And it is preferable that he adds the words
wa raḥmatul lāhi wa barakātuh
and Allah’s mercy and His blessings (be upon you too).