Here are some phonological rules that commonly apply to American English. Of course, not every American speaker may use them all. I have included pointers to the similar set of rules offered by P. Ladefoged in his A Course in Phonetics, 5th Edition (Harcourt, Brace, Jovanovich, 2001). My notation for rules is based on the Chomsky&Halle notation conventions.
(1) aspiration
[-voice] stops -> aspirated / + __ [V or glide] [-voice] stops -> unaspirated /elsewhere
(where + is a syllable boundary) That is, a voiceless stop that does not associate with the preceding syllable but is syllable initial becomes aspirated. Notice tap and trap have aspirated t but not strap and lapdog. Cf. Ladefoged CiP5, p. 72, Rules 2 and 5.
(2) vowel duration
V -> longer duration / __ [+voice C], or syllable finally
Notice bat vs. ban, bar, boo and boo'd. Cf. Ladefoged, CiP5, p.98 , Rule 1.
(3) glottal stop
/t/ (and sometimes /p,k/) -> [?] /__ [+] or /__ N
(where [+] is syllable boundary and [?] = glottal stop). That is, voiceless stops, especially [t], are glottalized when syllable-final or before nasals. Notice Pat, butler (yet not buttress since the t is resyllabified ), cotton, Courtney, Batman. Cf. Ladefoged, CiP, p. 72-3, Rule 9, 10.
(4) dental assimilation
[alveolar] -> [dental] / __ [dental] (even across word boundaries)
Notice panther, in the Y, width, at the Y, wealthy, fill the Y. But does not apply to sibilants, [s] and [z]. Cf. Ladefoged, CiP, p. 74, Rule 14.
(5) flapping
[apical stop] -> [flap] / sonorant __ V-unstressed] [apical stop] -> [flap] / [-lateral] __ V-unstressed]
That is, when ambisyllabic, even across word boundaries.
Flaps are likely in bitter, murder, quarter, dentist (for most dialects but not NY City), humidity, say that again, but not in guilty, or attack. Nevertheless, a year ago today with two flaps is possible for me. Same with year ago tomorrow but never I just saw Thomas. Most likely, it is frequent expressions that allow word-initial flapping. Cf. Ladefoged, CiP, p. 74, Rule 13, 13a.
(6) stops nonreleased before any other consonant
stop -> unreleased / __ + C
Cf. apt, Ridley, labcoat, ad-man. Cf. Ladefoged, CiP, p. 72, Rule 8.
(7) liquids: `dark' (velarized, u-like tongue position) vs. `light' l (fronted, I-like tongue).
/l/ -> velarized / __ + ; elsewhere: light
Notice lift vs. pickle. Lil has both types. Cf. Ladefoged, CiP, p. 73, Rule 12, 12a.
(8) longer duration at end of word or phrase (Ladef, p. 98, Rule 1)
V -> lengthened / in phrase-final syllable
(9) vowel deletion in certain contexts (Ladef, p. 83, Rule 3)
unstressed V -> 0 / __ [l,r,N] and sometimes others
(where [0] means zero or no sound at all). Thus the resonant consonant becomes syllabic (that is, becomes the nucleus of its syllable. Notice sudden, cupful, police. In potato the aspiration interval alone will sometimes be the only vowel in the first syllable.
(10) vowels preceding a nasal are nasalized, especially in stressed syllables
V -> [+nasal] / __ N (in same syllable)
Notice ham vs. had; hunt, thank, can't, but connect (with no nasal vowels). Cf. Ladefoged, CiP, p. 99, Rule 5.
(11) nasal deletion, optional after vowel nasalization
N -> 0 / V _ C \|/ S
(where the tree attached to S means `V, N and C belong to the same syllable' and the C is voiceless, so deletion may occur when N is in a final consonant cluster). Notice the possible absence of a nasal consonant segment in thank, camper but not band, lumber, sinner, or tan. The vowel is strongly nasalized, but the nasal consonant practically or completely disappears before the voiceless stop.