My cartomiser tastes burnt.

This may be because the wicking material has gotten too dry and is starting to burn. Refilling the e-liquid in the cartomizer may remove this burnt taste, but if not, then it's time to change to a new cart.

My cartomizer isn't giving me any vapour.

As above, this could be because the cart doesn't have enough liquid inside it to efficiently vapourise. You can try refilling the cartomizer, or switching to a new one. You may also need to recharge your battery.