For clarification I have a Samsung Galaxy Note 3 that in theory can charge wirelessly. It uses the Qi (pronounced "chee") standard which provides an inductive charge, this is a convenient and hassle free way to charge your phone.
The first stumbling block I found was that my Samsung Note 3 handset didn't ship with the correct back plate to wirelessly charge. It appears as though this wasn't an omission or product error, it seems to be firmly be Samsung's strategy. I'm confident about this as both the Galaxy S4 and Galaxy S5 are wireless charger compatible but neither ships with a back plate that allows them to charge out of the box.
So the first step to Qi compatibility is to switch out the standard back plate and fit a Qi wireless charging compatible case. Something like this: http://www.amazon.co.uk/Samsung-S-View-Wireless-Charging-Galaxy-Black/dp/B00FON947S/ref=sr_1_1?ie=UTF8&qid=1407157846&sr=8-1&keywords=samsung+note+3+wireless+charge+case
Or as an alternative you could install a bridging 'card' which has a coil in it to enable Qi charging. This is effectively the coil that comes inside the Samsung Qi wireless case. Link: http://www.amazon.co.uk/Ultra-thin-Wireless-Charging-Receiver-Samsung/dp/B00GFGL0XE/ref=cm_cr_pr_product_top
Now the handset should be Qi compatible. Keep an eye on some of the coil cards that you can pick up as some of them are NFC compatible and some as S-View, but there doesn't seem to be a Qi /NFC / S-View coil card out there.
Finally find yourself a Qi charging plate. The choice here is extensive but the main difference seems to be voltage and cosmetics. Simply find a plate that is the right size and shape for you. Here's a selection: http://www.amazon.co.uk/s/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=samsung%20note%203%20wireless%20charge%20pad
So in summary the handset is compatible with Qi, but it doesn't work out of the box. You need further accessories to enable Qi wireless charging, and you need to buy the charging plate. The Qi standard is evolving as well, the standard has just been upgraded: http://www.theregister.co.uk/2014/08/01/qi_wireless_charging_extends_to_30mm/ so it might be worth waiting for the next wave of devices.