Can someone provide an example where I can use count to count the rows in columns meeting different criteria?

Example: I want to count the number of rows that have a value of zero in a column, and I want to count the number of rows in the same column with a different value.

I tried something similar to:

Select
Count ( Select Column1 From Table1 where criteria1 = 0) as First ,
Count ( Select Column1 From Table1 where criteria1 <> 0) as Second

From Table1

Where criteria2 = something and criteria3 = somethingelse

I can't seem to get it to work, but I'm just a hack when it comes to SQL.