One of the worst things to do is overfill and try to vape it back to normal. For instance, if you hold up the carto to some light and you can clearly see through it, then you haven't flooded it. If you can't see into it, that means it's flooded. Very gently blow out the excess
juice. If you try to vape the excess it could easily over-do the carto, and it won't vape right. This is just from my own experience, since I just had to toss out two cartos because I tried to vape through the flooded carto.
I've never used a syringe to fill them. A much easier way is to just directly drip onto the filler. I fill my cartos by taking off the soft cap of my cartos. I hold them at a 45º angle and drip 2 drops, then turn it. After about 12 drops, I let it soak up a bit, then I do it again. Once it's nice and "slushy" on the top, it's good to go. I have a carto of Peach from Vaporbomb (very thin liquid; thick liquid and cartos don't mix all that well) that's on two weeks and still doing pretty well. I'm on about a week with my Arctic Ice and Strawberry cartos as well.

You'll get the hang of it, even if it's a PITA.
My cartos are from: LiteCigUSA, Liberty-Flights, or from sweet-vapes.com(only when I make a juice order, though).