Are you having problems with the values in the drop down list or your script?
Are the values from a custom value list or do you have a value list with the "specify values from a field" option?
Or do you just want a button you can click to "find this year's records"?
Try this as a script
set variable $_year = "*/*/" & year(get(currentdate))
Create a perform find script step --
Click on DateField and in the text box enter $_year
save the setup
The two step find for this year should work or need revising a bit...
I prefer this form of the same script
Enter Find mode 
Set field [Yourtable::YourDateField ; Year ( get ( CurrentDate ) ) ]
Set Error Capture [on]
It's a few more steps, but makes it much easier to see what criteria is being specified when you review the script at a later date. (Don't have to open up the perform Find step to see what was specified.)
But it's only one possible solutions for what Gavjuan is requesting.
It's also possible to set up a value list of years based on the data entered into this same table and thus it will update to list every year for which there is at lest one record in the table--including the current year.