Many individuals I have worked with on accents need some help with the /th/ sound. The bad news is, there are actually two different /th/ sounds in English. If you were unaware of this, you are not alone! Many whom I work with are unaware of this distinction before I point it out to them.
To explain this fully, I need to first explain the difference between “voiced” and “unvoiced” (or “voiceless”) sounds. I will illustrate with an example. Please place your fingers on the front of your throat, over your Adam’s apple. Say /s/ (when I put a letter between slashes, it means to say the sound, not the letter. So please say “sssss,” not “ess”.) Done that? Ok, now say /z/. Feel any difference? That’s your voicebox, or larynx, making a sound for /z/ or not for /s/. Now do it again and think about what your tongue is doing when you say /s/ and when you say /z/. You will notice that it is doing the exact same thing for both sounds. Cool, huh? So the only difference between /s/ and /z/ is their voicing — /s/ is unvoiced, and /z/ is voiced. There are many other pairs of sounds like this in English as well as all other languages.
Why am I telling you all this? Because this applies to the two /th/ sounds in English. One is unvoiced, and one is voiced. They are both produced just as you thought — with your tongue placed between your teeth. But there is /θ/, the voiceless /th/, as in think or bath; and there is /ð/, the voiced /th/, as in the or mother.
If you were unaware of the existence of two different /th/ sounds, you may be surprised and alarmed about how you will ever figure all this out. Now, here’s the good news: you already know which is which! Really. Trust me. You know the difference. You may not be making the /th/ sounds correctly, but I promise you, you are not confusing the voiced and voiceless sounds. This would be a lot easier to show you in person, but let me try to explain by way of example.
Most Russian speakers who err on /th/ would say the following:
I sink zat was her muzzer at ze store
I think that was her mother at the store.
Get it? For the voiceless /th/ in think, the Russian speaker substitutes /s/, a voiceless sound. For the voiced /th/ in that, mother, and the, the Russian speaker substitutes /z/, a voiced sound. They know which sound is which, and their substitutions are always consistent with the voicing of the sound. This is similarly true for other accents. Some speakers substitute /t/ and/d/ rather than /s/ and /z/ for /θ/ and /ð/, but trust me, I have never encountered a speaker who did not know which was which.
So how do you make these two sounds? The good news is, just remember to put your tongue between your teeth. Beyond that, it can get tricky and a bit of instruction as to how to get the /th/’s to sound right may be necessary. But putting your tongue between your teeth is a good place to start. Just rest assured — you know which /th/ is which!