How do I efficiently lower my karma?

By far the simplest way to acquire Bad Karma in Fallout 3, provided you have the Broken Steel add-on installed, is to take the Devil's Highway perk. It instantly sets your karma to the bare minimum of -2000. ...However, it can only be taken starting level 24, so it's not exactly an option for early-game karma farming.

Some simpler, repeatable options for karma loss include:

• Use of the Mesmetron. Nameless NPCs can be enslaved for -100 karma a pop, regardless of the enslaved character's karma (ie, enslaving raiders is considered just as evil as enslaving innocent civilians). This is normally a bit dicey because of the 50% chance they'll either attack you or explode and the need to replenish your collar supply with each victim, but it can actually be farmed fairly easily by a method described in the wiki page for the collars. This is probably the easiest way to go about farming bad karma provided you're in a position to progress the Paradise Falls questline far enough to get the Mesmetron and some collars:

It is possible to turn hostile unnamed non-player characters (e.g. raiders) into friendly characters by first enslaving them and then instantly removing the slave collar. A Science skill of 75 or higher is recommended. Afterwards the player will again have the slave collar in their inventory, which can be used to enslave other non-player characters.

This procedure however, results in a lot of bad karma for the player. It is an effective means to accumulate bad karma without actually being bad. The removal of the slave collar does not reward positive karma if the player has enslaved the character. [Source]

• Theft. Each discrete 'theft' is -5 karma (so, stealing five owned items out of a container at once is -5 karma, but opening an owned box 5 times and stealing an item out of it each time is -25 karma). Items stolen from owned containers can be put back and stolen again for even more karma loss, resulting in a somewhat tedious but very simple way of farming bad karma.
• Paulie Canelli. This Rivet City trader will beg Psycho off you, and for each you give him you'll get a -100 karma hit. Note that he will die eventually if you give him even one dose, but if you stuff your pockets full of Psycho and gift him as much as you can before he keels over, you can get a pretty hefty karma loss for the price of one (very minor) named NPC's life.
• Cannibal perk. Only -1 karma per corpse guzzled, so it's not such a good primary method, but you're probably going to be killing a lot of people in this game anyway so it's a decent perk to take if you want to make sure you always have a way to drop your karma just that little bit more. (Plus, it just feels evil.)

The FO3 wiki page on karma has a list of many more ways to get negative karma in the game if you're looking for more options, but many of the ones listed there are either one-time-only or involve a lot of murdering of named NPCs.