How do I add a current date to date field?

Move your code to a doc-level script, via Tools - JavaScript - Document JavaScripts. Create a new item there called "scripts", delete the function that is created by default and paste your code, and you're done.

However, be advised this will overwrite any input the user entered into the field the next time they open the file.

If you don't want to do that then add this before the first second line:

if (f.valueAsString=="")

But then it would not update the field, even if the user didn't enter anything into it... Basically it will only update it if the field was empty when the file was opened.

For validate script you need to change field value for the script to trigger, so either use under calculate tab or as one of the action (Mouse UP) it all depends on how you wish to trigger script and if you wish script to update date or remain fixed.

Also, you can shorten script like this: event.value = util.printd("m/d/yyyy", new Date());

If you use as action script, change event.value to event.target.value