After finishing salah what should be reciting next? and are you meant to do dhikr after each fard prayer?
You can do various forms of dhikr or dua. The most common dhikr, which is done after every prayer, is to say subhanAllah 33 times, alhamdulillah 33 times, and allahu akbar 34 times, mentioned in Sahih Bukhari and Muslim.
Ka'b b. 'Ujra reported Allah's Messenger (ﷺ) as saying:
There are certain sayings, the repeaters of which or the performers of which after every prescribed prayer will never be caused disappointment: "Glory be to Allah" (subhanAllah) thirty-three times." Praise be to Allah" (alhamdulillah) thirty-three times, and" Allah is most Great" (allahu akbar) thirty-four times. (Sahih Muslim 596 a)
You can also shorten these to ten each, mentioned in a number of hadiths, for example:
'Abdullah ibn 'Amr reported that the Prophet, may Allah bless him and grant him peace, said, "If a Muslim man persists in two actions, he will enter the Garden. They are easy, but those who do them are few.' He was asked, 'What are they, may Allah bless him and grant him peace?' He said, 'That you say "allahu akbar" ten times, "alhamdulillah" ten times, and "subhanAllah" ten times after every prayer. ...
(Al-Adab Al-Mufrad, Book 50, Hadith 1216, authenticated by al-Albani)
You can also recite any other dhikr words you know if you choose.
After that, you can perform dua, or stand up to pray the voluntary salah, if there is a voluntary salah associated with the obligatory one.