I don't think of it as refilling. I think of it as keep them damp. Because if you don't keep a carto damp, then you might singe the stuffing and ruin its flavor.
Filling and adding juices depends on the kind of carto you got.
If you got some kind of reservoir cato like Joyetech or CE2/Clearomizer/Fluximizer then you need the kind of syringe they want. I think the Joyetech ones want a sharp syringe and the others want either their special flexible syringe tip or a blunt syringe. I don't use any of these so someone else will have to help you if that is what you got.
I only use stuffing-type cartos with soft cap and defined center air channels like Boge for 510, and Vapor4Life for my KR808D-1.
How I fill a blank:
Pop out the soft cap with an unbent paperclip in the mouth hole, very careful not to catch stuffing or the wire loop.
Shake and open the eliquid
Hold a bit of tissue on the threaded end hole, tilt the carto, and add 18+ drops per ml of capacity into the stuffing (Boges are about 1ml)
Clean up the threaded end, tilt open end down into tissue, puff into threaded end to clear air channel (Boges have a defined center air channel and I want to see light through that)
Sop up any loose juice above the stuffing
Cap and let it settle - I lay it on different sides for 15-20 minutes to make sure every bit of stuffing gets damp so I won't singe the carto. if you use thicker juice than me (I use 20% Vg or less) then you may need to wait much longer.
How I refill:
While vaping, if the vapor gets a bit light or a bit dry or the carto is getting hotter than normal, I take the carto off the battery and add eliquid. I sometimes use a plastic or delrin drip tip as a mouthpiece on Boge cartos (not to drip into since the juice would head for the central air channel)
I use manual batteries only and they are safer from being damaged by carto leaks. If I am using a prefill and I have the same liquid, I may check if it needs a bit more liquid before I even start using it. Many prefills are lightly filled.
Longevity - I can get 1-2 weeks or more good use out of a 510 Boge carto if I fill with very thin clear juice. I think the juice I am using has no more than 10% VG (it's a Vapor4Life WOW juice - WOWbacco - very thin and very clear but it does make a bit more vapor than pure PG). I get a week or more good use from a Vapor4Life WOW carto filling with a combination of WOW Vanilla and Gourment Vapor 80pg/20vg vanillarum. I find both higher VG and sediment from some darker juice flavorings can clog the stuffing of a carto and make it sluggish for wicking and for airflow.