The simple answer is no. Not only doesn't the Bible say how we should celebrate these events, it doesn't even say that we should. Even ignoring the most obviously pagan factors such as decorated trees and yule logs, many of the traditions we follow today go directly against what the Bible actually does say about it.
The most obviously wrong thing is the date. Even in the Middle East, winter can be cold and wet, so with shepherds out in the fields tending their flocks by night, it isn't possible that it would have been in December. The timing of Jesus's and John's births, along with the schedule for Zacharias's priestly duties, can be used to calculate that it would have occurred around September or October, possibly at the beginning of the Feast of Tabernacles.
The celebration of birthdays is not promoted by the Bible. In fact, the few times that birthday celebrations are mentioned, they are very unwholesome events, such as when John the Baptist's head was presented on a platter as a birthday gift.
Even the events that we do take from the Bible we tend to get wrong.
How many wise men visited Jesus in the manger: three, several, or zero?
We traditionally assume three, and the We Three Kings
song
even assigns them personal names, but the Bible nowhere says how
many wise men there were.
Yet even several
is also a wrong answer.
This was a trick question.
The wise men visited the child not at his birth place, but at his house,
possibly a year or so later.
It's historically inaccurate, but moving their appearance
to the time and place of birth makes a far better story,
especially if that place itself is gratuitously moved
from a house into a stable.
There is one Biblical passage that I can't help but imagine being read by Linus, as Charley Brown and his dog Snoopy walk into the woods, cut down a tree, bring it home, and decorate it:
Thus saith the LORD, Learn not the way of the heathen, and be not dismayed at the signs of heaven; for the heathen are dismayed at them. For the customs of the people [are] vain: for [one] cutteth a tree out of the forest, the work of the hands of the workman, with the axe. They deck it with silver and with gold; they fasten it with nails and with hammers, that it move not.— Jeremiah 10:2-4