The T in "water" and "motor" and "a lot of" should (typically) be pronounced with the tip of your tongue against the back of your top row of teeth. This is called an "unvoiced consonant" (you're pronouncing the word by forming your tongue and exhaling air, not by vibrating your vocal chords). In many dialects, however, the T can sound like a D for many words (like the example Robert gave). Because English can be spoken very quickly and words run together, or sounds are compromised, "water" can sound like "wadder," and the listener wouldn't question that--you sound normal saying "waTer" or "wadder." When the T sound turns into a D sound, it's then called a "voiced consonant," meaning you're still placing your tongue in the same position, but instead of exhaling air to make the sound, you vibrate your vocal chords. Many consonants have letters that can demonstrate this: B is a voiced consonant when you vibrate your chords to make the B sound in "begin." P is an unvoiced consonant because you don't vibrate your chords to make the sound of P in the word "supper," but you form your mouth the same way for each letter. You also form your mouth in the same way for each of the following voiced/unvoiced pairs: V is voiced because you vibrate your vocal chords, as when pronouncing "victory." F is unvoiced because you exhale and don't vibrate your vocal chords when pronouncing the word "family." G is voiced because you vibrate your vocal chords, as when pronouncing "gone." K is unvoiced because you exhale and don't vibrate your vocal chords when pronouncing the word "kite." Z is voiced because you vibrate your vocal chords, as when pronouncing "zebra." S is unvoiced because you exhale and don't vibrate your vocal chords when pronouncing the word "silly."

A double T in the middle of a word becomes a soft 'D' sound. I come from Seattle, we pronounced it 'See-Ah-dull', the 'Ah' as in 'Adam'.

I would say in american english, little is pronounced like "leedall"

Usually, it's a "flip the tip of your tongue against the roof of your mouth" type sound, but, in some American dialects, the "t" sounds like "d" in some of these words or isn't pronounced at all.