This is an awkward question because the answer is basically “nothing”.
The New Testament teaches prayer to God:
In that day you will no longer ask me anything. Very truly I tell you, my Father will give you whatever you ask in my name. (John 16:23)
Do not be anxious about anything, but in every situation, by prayer and petition, with thanksgiving, present your requests to God. (Philippians 4:6 NIV)
There are of course two examples of people speaking to Jesus: Stephen and Paul in the visions they had of Jesus. But no examples of prayer.
By the same token, although the New Testament only teaches prayer to God, and this is the norm documented in the New Testament congregations, the New Testament also does not explicitly forbid personal conversation with Jesus – and many people in private find talking to Jesus helpful.