The "th" Sound
Many non-native speakers have difficulty with the "th" sound. It just does not exist in that many other languages. Greek has it; Icelandic is the only other Germanic language that still has it. It was changed from a fricative to a stop in German and the Scandinavian languages (Grimm's Law, for all you have taken a linguistics class), and other dialects have variations of it. The sound has an interesting and complex history...
But let's cut to the chase for people struggling with this sound; how do you produce it correctly and SEAL the DEAL?
You need to place your tongue between your lower and upper teeth. You also need to breathe out air while your tongue is in that position. If you just place your tongue in the right position but don't blow simultaneously, the sound becomes stopped/distorted. "Thing" might sound like "ting" and "that" might sound like "dat."
Try putting your tongue between your teeth and prolonging the outbreath. Just get used to the feeling first, then try it with various vowel sounds: thhhhiiii... then in a real word: thhhiiiiss... then in a phrase: thhiiss will work! To a lot of people, it feels unnatural to stick your tongue out and blow in someone's face- get used to it! Then, try practicing with minimal pairs: then/den, those/doze; thank/tank, thin/tin. (Or practice comparing it with whatever sound you are substituting it with- thank/fank, etc.) Then you have to practice linking it with other sounds in connected speech.
Also- the difference between the two /th/ sounds is that the /th/ sound in "think" is voiceless (your vocal folds aren't vibrating) and the /th/ in "the" is voiced- place your hand on your throat and you will feel the vibration.
You have to practice this sound in everyday conversation. It is such a frequent sound- the, they, that, them... so you have plenty of opportunity. Try it on your next shopping trip. "Do these come in other colors?"
For a free pdf and audio download to help you practice and master the "th" sound, contact me and write "TH Sound!"