yīyuè
January
Chinese months have no names, only numbers: a digit plus 月 ("moon, month"). January is 一月, December is 十二月.
yí ge yuè
One month
liǎng ge yuè
Two months
zhège yuè
This month
shàng ge yuè
Last month
xià ge yuè
Next month
xiànzài jǐ yuè?
What month is it?
January is 一月 (yīyuè), literally "month one".
December is 十二月 (shí'èryuè), the twelfth month.
一月 is the name of the month, January. 一个月 is a length of time, one month: 我学了一个月 means "I studied for a month".
Tomyo
Numbers stick when you use them. Tomyo reviews your words on a schedule so what you learn is still there a month later.