How to ORDER a big table? I have a simple but big table (tens of millions of rows). The performance is quite good except when I need to order the table by the column with format datetime.

A simple SELECT query to fetch the last 10 updated rows takes tens of seconds.

Is there a trick to order big table in a fast way?
MySQL recommends using indexes for a variety of reasons including elimination of rows between conditions: How MySQL uses Indexes.

This makes your datetime column an excellent candidate for an index if you are going to be using it in conditions frequently in queries. If your only condition is BETWEEN NOW() AND DATE_ADD(NOW(), INTERVAL 30 DAY) and you have no other index in the condition, MySQL will have to do a full table scan on every query. I'm not sure how many rows are generated in 30 days, but as long as it's less than about 1/3 of the total rows it will be more efficient to use an index on the column.

Your question about creating an efficient database is very broad. I'd say to just make sure that it's normalized and all appropriate columns are indexed (i.e. ones used in joins and where clauses).