Sometimes students use ‘the next next day’ or ‘the day before before’. This isn’t very good English.

If talking about the day after tomorrow, you can say:
‘the day after tomorrow’
‘in 2 days time’

If talking about the day before yesterday:
‘the day before yesterday’
‘2 days ago’

If counting forward from a day in the future or past (e.g. On the 19th I will go to Beijing. The next day I will go to Xi’an. The next next day I will go to Xining.):
‘the day after that’

If counting backwards from a day in the future or past (e.g. On the 20th I will go to Xining. The day before I will go to Xi’an. The day before before I will go to Beijing):
‘the day before that’