Local (non-Danish) census records for your ancestor may say the year in which he immigrated.
With that information your next step is to find a ship record/immigration record on ancestry.com for your ancestor. It will provide you with the name of the ship he traveled on and the date of arrival to his new country. If any of your ancestors children were born in Denmark and he traveled with them it can help confirm you are looking at the right ship record. Also if he was married in Denmark, he should be traveling with his wife, which can also confirm you are looking at the right ship record. Once you've found the right ship record, you will know the date which your ancestor traveled and his ship's name.
Danish Emigration Recordshttp://www.emiarch.dk/search.php3?l=en
Using your knowledge of the ship name and date of arrival you should then try to find your ancestor in the Danish emigration records at the above link, it will give you his last residence in Denmark.
Indexed Census Recordshttp://ddd.dda.dk/ddd_en.htm
Then by knowing his last residence you can search that town for his census record, which might give you parents/siblings/place of birth, approximate birth years, etc
Unindexed Church Parish Records and Census Recordshttp://www.sa.dk/ao/English/default.aspx
Once you have place of birth of your ancestor, then you will manually have to search images of parish records for his birth/marriage/death record. Birth record will provide his parents names, then you can repeat the process on his parents but skipping the emigration/immigration steps.
This will allow you to search further and further back and it allowed me to get my family tree back to the 1700's in Denmark.
Good luck, you will probably need assistance reading the parish records, but there are very helpful folks here.