Salt is the essentially the "mana" portion of abilities in Bioshock: Infinite. In what ways can I get more salt? Are there any ways besides looting corpses and boxes for vials?
To add to the other answers, Elizabeth will occasionally give you Salts. More details behind that as mentioned in the answer(s) to this question: How does Elizabeth getting various loot and then giving it to you work?
Also, from the BioShock wiki, "Salts" article:
...certain beverages such as coffee and soda will also replenish a small portion of the player's Salts, while drinking alcohol will consume a small amount. Smoking cigarettes will also increase the player's Salts, though at a cost to their health.
Watch out for Salt Machines that will refill 100% of your Salts, free of charge and can be used repeatedly:
You can replenish your Salts (health and ammo as well) at Dollar Bill vending machines completely (100%) for $67 or partially (25%) for $19.
I recommend upgrading your Salt capacity to 10 before upgrading on your health or shields.
Be on the lookout for vest gear with "Blood to Salt", allows your enemies give Salts upon death 40% of the time.