What's the best way to dispose of used batteries?

Depending on where you live, you may be able to dispose of some of your batteries (alkalines) with the rest of your garbage, but chances are that you will have to use either a battery recycling dropoff program or dispose of most, if not all, of them (particularly NiCd, NMH and Li-ion) at a household hazardous waste depot. For more information:

The answer to your first question is largely dependent on where you live. In my opinion, New York is the golden standard. Their batteries are typically collected at designated centers depending on the type. Centers put them through a recycling process to recover lithium, nickel, cadmium, lead, etc. Rare-Earth metals are especially sought after for obvious reasons. On the other hand, alkaline batteries are considered safe and can be disposed along with household trash. Note: it is recommended that you keep lithium batteries away from water sources as they can react violently. Lead-acid batteries should be stored upright as they can leak highly corrosive sulfuric acid (this happened to a friend of mine). Smaller batteries, especially the nickel-cadmium type, should be kept away from small children as they are extremely harmful if swallowed. Sources: http://www1.nyc.gov/assets/dsny/zerowaste/residents/batteries.shtml, http://www.mass.gov/eea/agencies/massdep/recycle/hazardous/household-batteries.html, https://en.wikipedia.org/wiki/Battery_recycling#Lead-acid_batteries

These days, most batteries are for the rechargeable, but people still use good old fashioned AAs from time for you time. Alkaline batteries produced after 1994 can go straight into the trash, but lithium, button, and rechargeable batteries (including car or motor boat batteries) must be recycled because they contain toxic or reactive chemicals. Collect old batteries and bring them to a municipal hazardous household waste disposal center. There are lots of online resources and companies which make battery recycling even easier.