The file is created on one of our servers, and you don't have to do anything to create it! Just name each counter with a unique name; we prefer the format username-countername.dat. Do NOT call your counter 'username-countername.dat' - you should combine your username (let's say 'foo') with a countername (say 'index' for your main page. The countername is arbitrary but should be different for each page you put a counter on.
So in this example, your counter would be 'foo-index.dat'.
Also note that the counter code as listed doesn't work perfectly with all styles - the best way to get the code for a particular counter is to look at the sample you like on http://counter.dreamhost.com/ and then right click on it and open it in a new window. Switch the URL in the counter code with that URL, but replace sample.dat with your countername.
If you want to make the counter hidden, you can set the image size to something really small (say 2 pixels x 2 pixels) and then just bookmark the URL of the actual counter.
Hope that makes sense; contact us at support if you have any difficulties getting your counter working.