So with the 510 you can purchase either liquid or pre-filled carts? Is liquid the more popular option? And if you purchase the liquid instead, do you have to buy a different cart filler that doesn't dry out as quickly or can you reuse the pre-filled carts?
Liquid is the most popular option - easy to change flavors and it's less expensive in the long run.
You've gotten good advice here. On refilling the cartridge, do this - refill until you see a smooth bubble of ejuice on the top without overflowing it. This is 'too much', so take a paper towel and draw some of the ejuice off of the top of the cart until there's no more bubble. Now the filler should be wet, but you can see some of the texture of the filler (where you couldn't when you had a bubble there ;-) That's how the filler should look after you refill.
One other thing that was mentioned but needs emphasis - when using the auto battery it isn't recommended to drip onto the atomizer bridge because for the auto battery to work, there is a hole in the center post that allows that battery to turn on via sound/suction. However, juice can also get through that hole and short the battery. Not so with the manual battery which should have no hole or the hole is sealed - so with the manual you can drip 1 or 2 drops onto the atomizer bridge.
If you're getting no vapor, the most common problem (other than the battery needs recharged) is that the atomizer if flooded. Remove the atomizer and blow it out from the batt end into a paper towel, then put 2 drops on the atomizer bridge and restart using the manual battery (because you dripped ;-). You might have to huff it a bit to restart - taking drags and puffing without inhaling until you see vapor then vape on.
With the auto battery, take longer, slow drags on it as if you're drinking a thick shake through a straw - works better for autos that way.
And at some point you might look into the 'straw mod':
http://www.e-cigarette-forum.com/forum/tips-tricks/11421-cart-mod-better-refilling.html
This allows you to refill with more drops and helps aid in the 'wicking' of the ejuice from the filler to the atomizer bridge.
Have fun!!