For THIN /θɪn/

1. Put the tip of your tongue slightly out between your upper teeth.
2. Put your hand on your larynx (in a sec we’ll see why).
3. Practice just passing the air current and saying “ssssss”. Since this sound is voiceless, you should not feel vibrations on your hand.
4. 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.
5. 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.