In certain words, the letters 'th' are pronounced just like in "the" or "clothes" — /ð/. But in a word such as "filthy", the sound changes (/θ/). Which sound is more common? When seeing 'th', would you naturally pronounce it like in "the" or like in "filthy"?
There are more 'exceptions to rules' than there are 'rules'; however, there are some general guidelines that might help you.
The ⟨th⟩ sounds are represented by [θ] and [ð] in the IPA (I'll be using these symbols from now on to refer to these sounds). [θ] is voiceless while [ð] is voiced. Voiced sounds are produced by vibrating the vocal folds, so there's a vibration in the throat. Voiceless sounds are produced without any vibration in the throat.
[θ] is the sound that you hear in think, while [ð] in that. Both of them are called dental fricatives, because they're articulated by putting the tip of the tongue behind the top teeth or by putting it between the top and bottom teeth.
General guidelines for ⟨th⟩ sounds
There are no hard and fast rules that I'm aware of, but here are some general guidelines you can stick to:
1. Word-initially: At the beginning of a word, the ⟨th⟩ is almost always /θ/ as in think, three, through, thirst etc.
Exceptions: in function words like this, that, though, the, those, these, thou etc., the th is /ð/. And in some proper nouns like Thomas, Thailand, Thames, it's /t/.
2. Word-finally: Nouns and adjectives that end with ⟨th⟩ usually have /θ/ as in breath, cloth, bath, health, width, loath, mouth, hearth, sooth, teeth etc.
Exceptions include tithe, lathe, lithe with /ð/. blithe can have either /ð/ or /θ/. booth has /ð/ in BrE but /θ/ in AmE.
Verbs usually have /ð/ and mostly end with -the. Examples: teethe, bathe, clothe, breathe, soothe etc (compare the corresponding nouns: teeth, bath, cloth, breath, sooth etc.)1. Although 'mouth' (verb) ends with -th, it's pronounced with /ð/.
Plurals of some nouns usually have /ð/, depending on the evolution of the word. Mouths, paths, truths, oaths—/ðz/ (compare corresponding singulars that end with /θ/).
3. Word-medially: Most native words have /ð/ word-medially (between vowels or voiced consonants) as in father, mother, northern, other, rather, further, weather, whether etc.
Some native words have /θ/ word-medially. The adjective suffix -y usually leaves the terminal /θ/ unchanged if the /θ/ is preceded by an L as in filthy, wealthy, healthy, stealthy etc. But if the /θ/ is preceded by an R, then the /θ/ is more likely to become /ð/ as in worthy, swarthy. (Consider 'earthy' an exception, SMH!). [Read this answer for more details]
Compound words in which the first element ends or the second element begins with ⟨th⟩ like any.thing, every.thing, bath.room etc., often have /θ/.
Most loan words from Greek, Latin, German etc., have /θ/ word-medially as in sympathy, pathetic, panther, authority, author etc.
[Simplified from Wikipedia]
1 - Whenever you see pairs like bath - bathe, cloth - clothe, breath - breathe, close (adj) - close (verb), belief - believe etc., in which one grammatical category has a voiced sound and the other has a voiceless, blame Old English. Adjectives/nouns usually have voiceless sounds while their corresponding verbs have voiced. It's because Old English had a phonetic property called 'intervocalic fricative voicing', where a fricative (f, th, s) became voiced when it occurred between vowels or voiced consonants. Old English was a heavily inflected and pretty phonetic language, for instance, 'bath' was bæþ while 'bathe' was baþian. The fricative þ was between vowels in baþian, so it became voiced. The endings were later on lost and we got 'bathe' with a diphthong!