What's the best way to get rid if tartar from teeth but at home?

You cannot: Sorry but tartar , know as calculus is impossible to remove yourself. Often anesthetic is necessary. Scalers are used by the dental hygienist below the gums while you may be able to "chip" off what is above the gunline , the most damaging part is subgingival ( below the gums). Even dental hygienists cannot remove their own tarter.

No possible: Sorry, but it's not easy to remove tartar from teeth. That's why there are dentists and dental hygienists to assist you. Once it is off, you can keep it from coming back with good oral hygiene practices such as thorough brushing and flossing. Please go see your dentist to get a "jump start" and then you can take over from there. Good luck!

At home???: Unless you know some good looking dental hygienist.... And can invite her over for dinner... I am not aware of any "best" way to remove tartar from your teeth outside of dental office... Sorry.

Tarter : By becoming a dentist or a hygienist, able to do your own cleanings. Tarter comes from your saliva. Calcium in our saliva gets deposited on the surface of our teeth over time. Some people form more tarter then others. Good home care can reduce tarter but it will not prevent it. Dentists and hygienists have the training for removing tarter off teeth without causing permanent damage to you.