Never down the drain. We've had a few incidents in my neighborhood where the sewer pipes were clogged with fat, and a few people's basements flooded with sewage as a result.

For fats that solidify, let them do so, then pitch them in your regular garbage. Chill grease in the fridge if you need to get it to harden up. For ones that don't solidify, pour them into a sealable (hopefully non-recyclable) bottle, and throw the whole container away with your regular garbage.

It's possible that your area might accept cooking fats & oils as part of a recycling effort. Ours does for motor oil