LED power supply— What am I not getting?

I enjoy messing around with electronics. I have no formal training, but I understand the basic concepts of a volt, an amp, an ohm, etc. and I can distinguish a cathode from an anode. But I can't seem to figure out how best to light some LEDs...

The LEDs themselves are nothing too special: white, yellow, red, green. I understand that they each require different voltages to operate correctly without cratering. I recently bought an LED "driver" that claimed to offer variable voltages between 2.5 and 12 volts. I don't know how that's possible, but whatever: I bought one. It seems to be putting out around 10.5 volts DC.

I bought some 390Ohm resistors, and hooked them up to this driver (I had visited a web site that calculated 390 ohms as about the correct resistance for a single yellow 20mAh LED). When I test the voltage on the other side of the resistor, it still says 10.5 volts. But I figured that this was somehow being managed by the resistor down to a level where my LEDs could handle it. I then hooked it up to one of my flickering yellow LEDs: it flickered twice, and then burned itself out.

No wonder at 10.5 volts, right? But then what purpose was the resistor playing in this set-up? I would never hook up 10.5 volts directly to any LED, but when I have visited a site that calculates a correct resistor for me and I get that resistor and I use it and my LEDs STILL end up burning up, I figure I just don't know what I am doing. I'd like to be able to convert my socket voltage (125V AC) down to one I can use for most any LED (2.2-2.4V DC) but I just don't know how to do that. I thought a resistor running off of a 10.5V transformer was the answer, and it clearly was not. Which is why I am here. Someone please tell me what I am doing wrong before I burn up any more LEDs. Thanks!

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