If they are normal 510 carts and not those bigger EGo/510 mega carts, then you can get precut blue foam stuffing cheap at strictlyejuice.com - just go there and search for foam
On a full fill, remove the foam, fill the juice cup 1/2 way (2/3 if you are daring it to leak), insert the foam tapered end first and press the foam down into the liquid (a unbent small smooth paperclip helps), reposition the foam at the top edge of the juice cup, and top off with 1-3 or more drops - whatever it needs to look just damp on top, not a puddle. While vaping, top off as needed. When topping off doesn't help, do another full fill.
Note - few people actually use atomizer and cartridges aka carts. And you cannot use them on a tank atty - won't wick right. People more often use a drip tip on an atty on a manual battery only to test juices. And use cartomizers for their favorite thinner juices. Cartomizers hold more liquid than a cart, need liquid less often, and in general provide a more consistent and troublefree vaping experience. However they have limited lives - I can usually get a week or more good use out of a Boge with thinner clearer juices (20% or less VG juices, and I avoid ones that leave a lot of flavoring sediment that clogs both cartos and attys)
Boge cartos are most popular but there are many other kinds including reservoir cartos that need a syringe to fill. I use the Boges - they can be filled with the normal dropper bottle. They come in different ohms. Slim batteries cannot use the hotter LR 2.0 ohms (may damage slim batteries). The standard resistance 2.8-3.2 ohm ohms can be used on both slim 510 and Ego. And if you can find them, the 2.5ohm can be used on both and will be warmer but use battery charge faster (not as fast as 2.0's). I use standard resistance and use them on my slim manuals and my Riva 510 (Ego clone).
You can find black standard resistance Boge 510 cartomizers at LiteCigUSA.net and Liberty-Flights.com (though they run out more often). And NiteLiteVapor sells the standard resistance ones in black, tan and white.
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How I fill a cartomizer (Vapor4Life for KR8 or Boge 510 for 510 which are all soft-cap w/ no inner seals and defined central air channel)
I use thin (20% or less VG) liquid or Vapor4Life WOW liquids, preferably clear liquids w/ no sediment
Filling a blank carto - I pop off the soft cap (unbent paperclip carefully in the mouth hole, not catching any wires or stuffing!). I hold some tissue against the threaded end hole. I tilt the carto and slowly drip 18 drops onto the inner wall of the carto so it slides down into the stuffing while I rotate the carto. Then I wait 15 seconds or so then I drip however many more drops the stuffing wants to soak up. Then I do clean-up. If it is leaking, I clean that up. Then I tilt the open end down into the tissue and puff hard a few times into the threaded end to clear any juice out of the central air channel (I want to see light through there). If it looks too wet above the stuffing, I gently touch a bit of tissue to the stuffing (otherwise that liquid will be gurgling or spitting in my mouth). Then since this was a fresh fill of a blank, I now let it settle. I lay the carto on different sides for 15-20 minutes. Then it should be ready to vape. If you use thicker juices than me, then you may need to let it settle longer.
As I am vaping - if the vapor gets a bit light or a bit dry or tastes bit off or the carto is getting unusually warm, I will take the carto off the battery, open it, add 6-8 drops or whatever it seems to want (I will either hold a bit of tissue against the threaded end hole just in case, or skimp on how many drops I add to make sure I avoid drips if I have no tissue). I check to make sure the threaded end is dry, give it a couple of puffs into the threaded end to make sure the air channel is clear, and continue to vape.
Note - it is easy for me to "open" my main cartos for adding juice because I replace the white end cap with a plastic or delrin drip tip (I get them at LiteCigUSA.net). So I can easily pull that out with my fingers when I add juice and it keeps my lips cool if the carto is hot.