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.