The Chinese dating system during the imperial years is difficult, and there are a few ways to denote it.

Primarily and most commonly used was the regnal year. This uses the Emperor's era name to denote years. The year was rendered like this example from imperial literature: "the first month of the thirteenth year of Jianyuan".

In regard to this, 1620 is actually a fascinating year, as it saw the reign of three different Emperors. The Wanli Era ended on August 28th after the long-reigning Wanli Emperor's death. The next era, the Taichang Era, ended less than a month later on September 26th, due to the Taichang Emperor's disease-induced death. The Tianqi Era picked up where the Taichang Era left off and continued for several more years. Depending on where you are in 1620, the era changes.

For month notations in eras, months don't reset with eras. Here's a (fictional) example: If the Tianchang Era ends in the sixth month of its 13th year, the following month would be called the seventh month of the first year of the Hongyuan Era. Eras also change when Emperors change their era names, which didn't really happen from the Ming Dynasty on (1368+). And, keep in mind, months are based on the Chinese system, with the first month beginning either in our January or February.

Another, less historically common way of denoting dates is the zodiac. As Chinese years are not 100% parallel with Gregorian years, which start and end on different days, the year 1620 was actually two different years on the zodiac. There were many starting dates used for the Chinese calendar, with their being no official one. These included the proclaimed starting year of the Yellow Emperor's reign, the year of Chinese unification under Qin Shi Huang, and others. Using the first of these, which may have been the most common, 4316 (Earth Goat) ended on February 4th, 1620 and gave way to 4317 (Earth Monkey).

There are also a few other incredibly esoteric ways scholars signified dates, making it clear just how complex calendars and dates really are. In covering the most predominant, though, I hope I answered your question!

If you're interested in reading more, there are a online resources (such as this: http://www2.ihp.sinica.edu.tw/file/1097kaBVwNb.pdf) that can provide some basic information, though sadly most of what we know about the Chinese calendar is recorded in Chinese language books. It really is a fascinatingly complex topic, though, and further proof that calendars are one of the most interesting human creations!