What you'll need in order to do this:
A) One full sized ship (no shuttles or you'll only earn 75% of what you could) equipped with a Borg engine.
B) A Federation captain with at least 6/9 in Driver Coil.
C) The mission Stranded In Space for use as a transwarp location.
D) Change your video settings to their lowest possible settings. This reduces load times and helps avoid the 95% bug (freezing at 95% when loading a new zone).
E) Change the setting under Options > Control > Keep moving during contact dialogues to On.
Helpful but not necessary to have:
1) Ventrilo and preferably a mic, just to make explaining things easier and faster.
2) Rank 3 or 4 in Diplomacy for Diplomatic Immunity.
3) A helpful Klingon friend who can grant Raiding Party, the KDF version of Diplomatic Immunity. This is definitely the least important aspect however, which is convenient since it's probably also the least likely to happen.
What you can expect after 1-2 practice runs:
1) 2 million ECs earned in one hour.
2) More diplomatic DOff missions than you likely have the personnel to run, which is great for helping you get to Diplomacy rank 3+ if you don't already have it.
If you're familiar enough with STO, you probably realize I'm talking about doing Tour the Universe. My first run after being shown this method earned 1 million ECs. That was with me not really knowing what I was doing for the first half hour, and getting the 95% bug four times. My second run I got 2 million ECs, and that was with not having Diplomatic Immunity for the first 20-25 minutes, and having three disconnects, the two of which combined cost me about 200k ECs. For comparison, if you follow the method outlined on STOwiki.org you'll get roughly two thirds what you could earn with the method that was shown to me.
Again, drop me a line if you're interested and we'll work out a time.