How to check sqlserver database which table updated

If you are talking about table structure then use,
for table modifiction

select Name,create_date,modify_date from sys.objects where type='u' 

you can fetch column update's date if column is primary key/foreign key like this

select Name,create_date,modify_date from sys.objects where type='p' or type='F'

for all columns modification date, you have to put trigger on table modification. and save entries inside a new table.

Note: when ever you will rename column table-modification trigger will not be fired. so, that case you will not able to save 'renamed' column's changes.

Happy Coding!
:)