Basically you should use SQL command ALTER like this:
using (DbConnection connection = new SqlConnection("Your connection string")) {
connection.Open();
using (DbCommand command = new SqlCommand("alter table [YourTableName] add [YourColumnName] int default 0 NOT NULL")) {
command.Connection = connection;
command.ExecuteNonQuery();
}
}
For more precisely answer we need more details like Maciej Los mentioned.