I had this problem a week ago on a vacation using my 1st beginner's DSLR ,a Nikon D40.
If its under Nikon Warantee,you can turn in to the dealer & wait for the repair but what if its beyond warantee period, or you bought it used with expired Warantee?
Here's my solution to fix it to save some repair charges and guess it might bless someone with the same problem there.
There is a gear motor that controls the tripping of the Shutter Release mechanism and over time,it either gets a bit tight to turn over or just contaminated with dust & needed soe light lubrication to get it back to normal( provided the motor is still ok).
Step 1: Tools & Stuffs You need
Small Watch Maker's Phillips Screw Driver
Can of Spray Grease (or any General Purpose Light duty Grease)
A Clean Dust free Environment
Step 2: First, remove its Battery.
You can recharge it if its is low for testing later.
Step 3: Remove the bottom base Cover Plate
This will expose the Gear motor operating the shutter which neede to be serviced .