Making the sound of 'th' in 'with'

Solution 1:

th in with is realized as a voiceless or unvoiced dental fricative, /θ/ as in think, or as a voiced dental fricative, /ð/ as in father, depending on the accent.

In Wells' Longman Pronunciation Dictionary, the poll conducted about the pronunciation of with gives the following results :

• AmE : wɪθ 84%, wɪð 16%
• BrE : wɪθ 15%, wɪð 85%

Wells adds that "in Britain /wɪθ/ is nevertheless frequent in Scotland (preferred by 82% of Scottish respondents) and that in some varieties, including GenAm but not RP, there may also be a weak form /wəð, wəθ/."

Here's Gimson's description of the sound in An Introduction to the Pronunciation of English:

• The tip and rims of the tongue make a light contact with the edge and inner surface of the incisors and a firmer contact with the upper side teeth, so that the air escaping between the forward surface of the tongue and the incisors causes friction. With some speakers, the tongue-tip may protrude between the teeth.

Solution 2:

In English, 'th' in 'with' is an unvoiced dental fricative, with the tip of the tongue against the back of the upper teeth. The lips are not involved at all. The wiki page mentions that it is sometimes pronounced 'interdentally', the tip of the tongue between the upper and lower teeth, but this is not done in English.

The sound is rare among the world's languages so it is difficult for most people learning English. In teaching, sometimes an exaggerated articulation is encouraged, where the tongue sticks out, making for all sorts of rude humor among kids. This helps with learning but is not the native articulation in English.