1) my first question: how do you pronounce "t" in words "better", "letter", "matter",..? like "d" or "t"?
North American speakers pronounce -tt- as [D], a dental flap. It's neither the sound [t] nor [d], but it sounds like them. To make the sound [D], say [d] but don't touch the back of your teeth with the tip of your tongue. Now say, be[D]er, le[D]er, ma[D]er.
Originally Posted by guest
2) my second question: do you pronounce "g" in "finding"?
No. The letters "ng" represent one sound, a nasal sound, a velar nasal. To make that sound, say [n] then raise the back of your tongue upward - not forward - to the roof of your mouth.
All these answers are true for certain dialects -- but not all.
Few native speakers give the "t" in "better" its full value. The standard US pronunciation has been described. In many dialects in the south of England, it is often pronounced as a so-called "glottal stop", although you shouldn't try to copy that pronunciation.
As for the "g" in finding, it is pronounced in some dialects, especially in the British Midlands (the Birmingham area). However, the Midlands accent is usually considered to be rather ugly.