When one of your clan members requests reinforcements, a message will pop up in your Clan Chat:
After tapping on "Donate", you may choose which of your troops and spells you wish to send to your clan mate's Clan Castle:
The troops will then be deducted from your camp, and travel to your Clan Mate's Castle. You will also gain experience points whenever you donate. Donating Spells becomes available at Clan Castle level 4 on Town Hall 8.
If you see troops or spells greyed out, it means that this troops can't be donated because it won't fit into your clan mate's Clan Castle.
If you see a troop's level indicator burning, it means that is is a max-level troop.
The "Donate Now!" button allows you to donate troops with a cost of Gems. You don't have to have these troops trained, and even if you do the troops won't be deducted from your army.
Remember: troops that defend your War Base in a Clan War are donated separately on the War Map.