If you already know the basics of how to tell time in Chinese, you may want to get a little more specific or sophisticated, using words like 分 (fēn) and 刻 (kè).
Minutes are marked with 分 (fēn) (short for 分钟 (fēnzhōng)). The way to include them in the time depends on whether they're minutes past or to the hour.
Minutes past the hour are expressed after 点 (diǎn) in the same way as half and quarter hours.
x 点 y 分
In Chinese, when the minute is under 10, the word 零 (líng) is often used after 点 (diǎn). For example, 2:07 would be said as “两点零七分” (liǎng diǎn líng qī fēn). However, note that when speaking, it is very common for most Chinese people take out the “分 (fēn)” at the end of the time.
x 点 零 y 分
In Chinese, quarter hours are only expressed on the 1st quarter x:15, and the third quarter x:45. Like half hours, they also come after the word 点 (diăn). We use the word 刻 (kè) to express "quarter hour."
x 点 y 刻
You can totally just use 十五分 (shíwǔ fēn) for "15 minutes (past)" or 四十五分 (sìshí-wǔ fēn) for "45 minutes (past)" if you're lazy, though. It also works!
When expressing how many minutes it will be till the next full hour, you put 差 (chā) in front of the time expression.
Minutes to the hour use this structure:
差 + Minutes + 分 + Hour + 点
or
Hour + 点 + 差 + Minutes + 分