I created a table and inserted 3 rows. Then I added a new column using alter.  How can I add values to the column without using any null values?
Update table table_name set column_name = value where 'condition'; 
I preferred to use p.key column for best result.
Two solutions.
this:
ALTER TABLE YourTable
ADD YourNewColumn INT NOT NULL
DEFAULT 10 
WITH VALUES;
null values first. Then update all rows to enter the values you want. Like so:
ALTER TABLE YourTable
ADD YourNewColumn INT NULL;
UPDATE YourTable SET YourNewColumn = 10; -- Or some more complex expression
Then, if you need to, alter the column to make it not null:
ALTER TABLE YourTable ALTER COLUMN YourNewColumn NOT NULL;
                                                                        Suppose you have a Employee table with these columns Employee_ID, Emp_Name,Emp_Email initially. Later you decide to add Emp_Department column to this table. To enter values to this column, you can use the following query :
Update *Table_Name* set *NewlyAddedColumnName*=Value where *Columname(primary key column)*=value
Example update TblEmployee set Emp_Department='Marketing' where Emp_ID='101'
suppose emp is the table and Comm is the new column then fire the below query .
update emp set Comm=5000 
                                                                           update table_name
   set new_column=value
                                                                        I think below SQL useful to you
update table_name set newly_added_column_name = value;