TL;DR: Purchase Y2 Thunderlord, equip it. Equip "upgrade machine rate" class item. Use 6 motes of light. Dismantle Thunderlord. Get 2 exotic shards.
Bonus SGA: Credit to aspergerac for posting the following in the comments below.
Also don't forget free exotics upgrades with the kiosks. If you have a 334 Exotic you want to infuse to 335 you will spend one exotic shard. If you break down that 334 instead you will get two exotic shards. Then you can use one shard to buy a new gun from the kiosk and the second shard to infuse it. This way you actually spend 0 shards instead of 1.