For THIN /θɪn/
- Put the tip of your tongue slightly out between your upper teeth.
- Put your hand on your larynx (in a sec we’ll see why).
- Practice just passing the air current and saying “ssssss”. Since this sound is voiceless, you should not feel vibrations on your hand.
- Now, while still “biting” your tongue say /t/. You’ll hear a mixture of /s/ and /t/. Repeat, but make sure there are no vibrations.
- Congratulations, that was /θ/.
For THE /ðə/
All as above, EXCEPT:
- Practice first with /z/.
- Pronounce /d/ and, very important:
- You should feel the vibrations, because this sound has a lot of energy.
- That was /ð/!
This is my reply to a question on English Language & Usage on Stackexchange. I hope it might help other people.