I use a syringe for dispensing, mixing DIYs, and injecting into my 510 carts, since I use a cart mod that does not fill well with dripping. A 510 cart takes, depending on the filler material, about 0.5 mL of liquid. However, if you are just filling carts that have stock filler in them (the poly wool that comes with most), generally you just add
juice until it is pooling up on top. Use the needle to sort of work out air bubbles. This may be less that 0.5 mL, from the volume of filler material, and also because the stock filler holds onto a fair amount of
juice without wicking it to the bridge, so it never fully empties.
Some people add a "vent straw", which is a coffee stirring straw cut so that the bottom is at the bottom of the cart, cut at an angle, and the top is just below the top of the cart, and its is put between the filler material and the inner wall of the cart. this becomes a very convenient injection port for adding
juice with syringe, and allows better circulation of the juice while you vape.