Auto-focus isn't working

You did not say which camera body you are using, but you probably have three different auto-focus modes on you camera. You might be using the wrong one.

The modes are as follows:
AF-A Mode: Camera automatically selects single-servo autofocus when AF-A subject is stationary, continuous-servo autofocus when subject is moving. Shutter can only be released if camera is able to focus. AF-S Mode: For stationary subjects. Focus locks when shutter-release button AF-S is pressed halfway. Shutter can only be released when in-focus indicator is displayed.
AF-C Mode: For moving subjects. Camera focuses continuously while AF-C shutter-release button is pressed halfway. Photographs can be taken even when in-focus indicator is not displayed.

The Nikon Coolpix is a compact digital camera that is well-suited for amateur to semi-professional photographers. Occasionally, some issues with the built-in flash can occur. If the hardware is damaged, the camera must be taken in for repairs. More often, problems occur because of obstructions or issues with the camera's settings and are easily repairable. Follow the troubleshooting guide to fix the built-in flash.

Instructions:
1.Ensure the Nikon Coolpix digital camera battery is fully charged.
2.Wait several seconds before pressing the shutter-release button if the "Flash Ready" indicator light is flashing red. Press the "Flash Mode" button once or twice to change the flash settings from "Off" to "On" or "Auto" if the "Flash Ready" indicator light is off.
3.Ensure there are no obstructions, like your finger or the camera strap, that are preventing the flash from firing if an error message appears on the display screen and the flash is not firing when the flash mode is set to automatic.
4.Press the flash back into the camera after every photo to ensure the flash always fires in "Auto" mode instead of just in low illumination settings. Press the flash back into the camera to turn off the flash in "Manual" mode; otherwise the flash will continually fire.
5.Change the auto focus setting from "Infinity" to "Auto," "Macro Closeup" or "Self-Timer" by pressing the "Focus Mode" button once, twice or three times to automatically turn the flash back on.
6.Use only Nikon external flash accessories to avoid damage to the built-in flash and camera circuits.

I hope you find it very helpful. Thanks.

you need to go into settings and change ur shutter settings to a quicker release. also dont hold down the button just press it real fast

This is a common situation with most compact point&shoot cameras. This "shutter lag" is because the camera has to do so much work when you press the shutter release button: focus on the subject, meter the light for proper exposure, and switch the electronics from viewing on the LCD to recording to memory. Larger (and more expensive) cameras have additional hardware to reduce this lag.

You can reduce the lag somewhat by anticipating the action. Press the shutter release button halfway to focus and meter. Keep it pressed halfway until the right moment, then press it the rest of the way to take the picture.

You can change this in the menu while in shooting mode. This is from page 48 of the manual:

Choose how the camera focuses.

A (auto) M d (Shooting menu) M I Autofocus mode

A Single AF (default setting)

The camera focuses when the shutter-release button is pressed halfway.

B Full-time AF

The camera focuses continuously until the shutter-release button is pressed down

halfway. Use with moving subjects. The sound of lens drive movement will be heard

while the camera focuses.

Hi,

Your Nikon Coolpix 3200 Digital Camera is equipped with a AF assist illuminator which makes focus easier when shooting in darker situations.

In spite of that, on occasion, it is quite possible that the camera will fail to achieve sharp auto-focus.

Point and Shoot cameras use a contrast-based focusing system: this works only when the contrast in the composition is high.

When you press the shutter halfway down the camera attempts to focus, but if it shows red brackets it implies that the focus has not been achieved.
Please take care to note this indication, and if you do not see the Green "Focus Lock" indicator, please attempt to recompose the shot.

Release the shutter, press halfway through again and wait for a focus lock.

The sensor on a P&S camera is very small (about 8-9x smaller in surface area compared to DSLRs)
In low light conditions achieving focus can be a challenge for P&S cameras.
These are technical limitations which are not specific to your camera but common to all cameras in the same segment across various camera manufacturers.

The lock that's around the 4-way button that moves the AF point will stop it from moving. The AF switch (says C,S,M) on the body below the lens release button gets knocked to manual and turns off the AF

check and see if the lense is in the macro mode

some cameras have a choice in menu as to monitor or continous autofocus-monitor or continous means camera always seeks a focus which hurts bat life but makes focus quicker-single means camera won't focus untill button pressed halfway-make sure you are not in macro mode-flower icon on screen-this will screw up focus except for close up work-good luck-check menu settings for your type of focus

I had the same problem. My issue was with all my lenses. I solved it by going to the menu and selecting the custom setting menu (pencil icon). Then from the right menu select the AE-L/AF-L and press OK. Then make sure it is set on AE/AF Lock. Presto...all my lenses worked on auto-focus.