You can buy items by left-clicking on them in the shop menu. 

Once you close the shop open your equipped/character stats interface and right-click on an item to drop it.  It will appear on the ground as a rotating treasure chest. 

Anyone can pick up the chest and the item within will be automatically equipped on them if they have room or don't already own the item  (Consumables can be stored in stacks of three) 

If the item is already owned or the player has no room then the item will be destroyed on pick up. 

Items can be sold back to the shop for 80% of their original value. 

Idols cannot be dropped

Feeding, trading, or reselling items has obvious applications.  The most common is having one teammate go back to base to load up on pots or teleport scrolls so that his ally(s) can stay in the field. 

Other uses I've seen or used -

1.  In a three person team, one assassin and two support generals, the support feed items to the assassin to outlevel his damage or tanking

2.  One player feeds the other an item he can sell to the store to buy idols

3.  All players on a team drop items that one player can use to buy an artifact or high-level citadel upgrade

4.  Players drop pots and other consumables just behind their first line of towers so that active item slots are free, to lessen the need to hit base, or to give fleeing teammates a needed ace in the hole

5.  New players feed experienced players who will be better able to use the gear/gold

Things to avoid when feeding items -

1.  Pick up an item you already have or don't have room for (the item will be destroyed)

2.  Attempt to exchange items when your opponents are anywhere nearby (nothing worse than dropping Slayer's Wraps for your teammate only to have an enemy pick them up)

3.  Attempt to drop an item while still in the shop interface (the item will be sold back)

4.  Feed teammates who don't need it or don't know how to use it
a. don't need - Support QoT is usually set with a helmet and some idol priests through midgame, you don't need to give her a Mageslayer because her role isn't DPS in most cases
b. don't know - Stacking items on the team UB when that UB doesn't know how to play yet tends to be a bad call

5.  Act as if you are as buffed as the guy you just spent all your gold equipping.  You aren't, so don't get out in front of him

6.  Expecting the feed to yield immediate invincibility for your team - it won't do that.  What it will do is create asymmetries most opponents aren't used to countering yet.

7.  Expecting the feed to bring your mediocre team to victory over a tight and organized set of opponents.  That won't happen, and they will exploit the asymmetries you present to them ruthlessly


*It's worth noting that PUGs can feed items as effectively as premades, they just have to take the first step and communicate.  If you join a random and someone suggests a feed strategy against a team that isn't noticeably better, go for it.   It's worth practicing. 

**Final Note:  The best of all possible ways to feed your teammates is to get (at least) the first citadel gold upgrade as soon as you have the war rank.  Don't leave it for your teammate to do if you can do it first.