without having the advantage of being able to look into your mouth, it's going to be difficult to determine what is causing your problem...or actually what your problem even is.
how long has it been since your last cleaning? a routine cleaning should remove all calculus (tartar) supragingivally (basically above the gumline) and maybe about 1-2 mm subgingivally. anything deeper than that is going to be more involved. if you just had your teeth cleaned, say, 2 days ago, and you feel they aren't clean, you should call your dentist and have them take a look at it.
everyone accumulates stain and tartar at different rates depending on several things. usually the three most common are intake (what you're eating), technique (how you're removing the bacteria from your mouth) and good ol' genes.
very common stain-relating substances are coffee, tea, tobacco, soy sauce, red wines, mustard, ketchup, berries, colas. if you're drinking 3 pots of coffee, and smoking like a chimney, you're going to get a lot of residue, that is going to be very difficult to get off at home.
as far as technique, always use a soft toothbrush. when you're flossing, make sure you're wrapping it around the teeth, making a "c" shape, trying to cover as much surface area as possible.
also, as the picture shows, get up under the gumline. this is where bacteria thrives, and if you don't get it out, the tissue is just going to stay inflammed and cause bigger problems than just stain. if they bleed, that's okay. healthy gums don't bleed. after a few weeks of doing this, they will toughen up and hopefully not bleed.
where are you noticing your problems? most people build up the most on their lower front four teeth, especially on the inside. there is a sublingual salivary gland (under your tongue) that helps cleanse the mouth, but it also can cause that area to harden bacteria on the inside surfaces of those teeth faster.
i can't really tell from here if it's actually STAIN, or tartar. if it's stain, you might want to try an automatic toothbrush, and if you're doing any of the previously mentioned staining habits, try brushing immediately after, or at least rinse with water until you can brush. if it's actual tartar (stain would be more brown, typically, tartar is very dry, chalky and has a more whitish, faint yellow tint), you may need to fine-tune your home care, and possibly go in more frequently for cleanings. we have patients who do that because they just like the feel of how clean their teeth are. tartar usually builds up dramatically in a 3 month period. because most people remove it effectively, they can get away with every six months (fucking 6 month recare was invented by a damn toothbrush commercial, not a dentist, btw). but if you want to go in sooner to arrest the buildup, talk to your dentist about it.
medications, health history and all sorts of other things can contribute as well. if you have any restorations or cavities in the areas you're noticing a problem, that could be your answer as well. if any restorations are rough, or have overhang/open margins, that's an area for bacteria to harbor and set up shop. things typically start as stain, and then progress from there to decay.
i don't know if any of this helps, but good luck and let me know if there are any further questions you have.
