I have the Ego-C as well, and I'm a newbie too... welcome to vaping and ECF.
As Rob said, you take a tank, pop the lid off (can be tough on your fingernails), fill the tank with juice but leaving about 1/8" of air space, pop the lid back on, push the tank in the bottom body firmly (should be "flush" with the outside), and you're ready. The atomizer, which is the thing with the spike on it, goes into the tank through the hole on the lid and wicks the liquid down to the atomizer. You don't "fill" the atomizer, the tank keeps the liquid flowing.
If this is a new atomizer, do a few quick but strong "puffs" (like you'd do with a tobacco pipe or a cigar when you're lighting it) without activating the battery to prime the wick and atomizer. Then activate the battery and draw, but don't inhale... do strong vapor draws like this a few times to clear out any priming fluid.
Regarding leaking, yeah, you will get a little (I do). But, it shouldn't be enough to get all over your hands and your couch. In my case, when I remove the tank I can see a few smears of liquid around the bottom ring where the atomizer spike sits, and I occasionally get a very small amount of it on my battery terminal. I just clean it up between tanks with a twisted tissue.
If you're getting more leaking than this, try another tank. Sometimes the holes in the lid don't puncture correctly by the atomizer spike. I find some tanks leak more than others, as I run several tanks with different flavors in them.
Finally, the beauty of the eGo is the standard 510 threading, so any 510 device will fit. If you don't like the tanks, you have cartomizers (like the Boge 2.0), clearomizers (like the GotVapes ones), etc. that you can switch to. Tons of options for that platform, and I'm in the "seeing what works for me" phase.
Hope this helps...