Dates are written by placing the character 日 after the day of the month you would like to specify.
Unfortunately, the dates have by far the most irregularities of any type of counter.
The 1st to the 10th, the 14th, the 17th, the 20th, the 24th and the 27th are all irregular.
For regular dates, the date is simply the number followed by 日.
For example, the 15th is 十五日 and the 31st is 三十一日.
Note that the Xth day and X days are said in the same way in Japanese for all numbers other than one.