Or, as I like to call it, hunting the wild Eth and Thorn (which are old letters that can be difficult to typesest), because back in the day, English had the two distinct “th” sounds represented differently in their writing system. There was one where you vibrated your vocal folds (that’s called ‘voiced’) which was written as “ð” and one where you didn’t (unvoiced) which was written as “þ”. It’s a bit like the difference between “s” and “z” in English today. Try it: you can say both “s” and “z” without moving your tongue a millimeter. Unfortunately, while the voiced and voiceless “th” sounds remain distinct, they’re now represented by the same “th” sequence. The difference between “thy” and “thigh”, for example, is the first sound, but the spelling doesn’t reflect that. (Yet another example of why English orthography is horrible.)
The fact that they’re written with the same letters even though they’re different sounds is only part of why they’re so hard to master. (That goes for native English speakers as well as those who are learning it as their second language: it’s one of the last sounds children learn.). The other part is that they’re relatively rare across languages. Standard Arabic Greek, some varieties of Spanish, Welsh and a smattering of other languages have them. If you happen to have a native language that doesn’ t have it, though, it’s tough to hear and harder to say. Don’t worry, though, linguistics can help!
I’m afraid the cartoon above may accurately express the difficulty of producing the “th” for non-native speakers of English, but the technique is somewhat questionable. So, the fancy technical term for the “th” sounds are the interdental fricatives. Why? Because there are two parts to making it. The first is the place of articulation, which means where you put your tongue. In this case, as you can probably guess (“inter-” between and “-dental” teeth), it goes in between your teeth. Gently!
The important thing about your tongue placement is that your tongue tip needs to be pressed lightly against the bottom of your top teeth. You need to create a small space to push air thorough, small enough that it makes a hissing sound as it escapes. That’s the “fricative” part. Fricatives are sounds where you force air through a small space and the air molecules start jostling each other and make a high-frequency hissing noise. Now, it won’t be as loud when you’re forcing air between your upper teeth and tongue as it is, for example, when you’re making an “s”, but it should still be noticeable.
So, to review, put the tip of your tongue against the bottom of your top teeth. Blow air through the thin space between your tongue and your teeth so that it creates a (not very loud) hissing sound. Now try voicing the sound (vibrating your vocal folds) as you do so. That’s it! You’ve got both of the English “th” sounds down.
If you’d like some more help, I really like this video, and it has some super-cool slow-motion videos. The lady who made it has a website focusing on English pronunciation which has some great resources. Good luck!