You can do a distinct count as follows:
SELECT COUNT(DISTINCT column_name) FROM table_name;
EDIT:
Following your clarification and update to the question, I see now that it's quite a different question than we'd originally thought. "DISTINCT" has special meaning in SQL. If I understand correctly, you want something like this:
Now you're probably going to want to use a subquery:
select COUNT(*) column_name FROM (SELECT DISTINCT column_name);
Let me know if this isn't quite what you're looking for.