A nasal sound is produced by lowering the velum to allow air to pass through the nasal cavity. Nasalization of vowels in English is an assimilatory process. In anticipation of a nasal consonant the soft palate lowers before the production of the nasal (and a complete closure of the oral cavity) and the result is that the preceding vowel becomes nasalized as well. So we might transcribe the word soon as [suũn]. The same can also occur after a nasal, so that you might expect news to be transcribed as [nũuz]. The velum may remain lowered for vowels occurring between two nasals as in [mũũn], so that the vowel is completely nasalized.
A common stereotype many people have about American English is that it’s very nasal and when trying to do an American dialect they nasalize all their vowels. This is an exaggeration in that, like Dutch, nasalization is determined contextually, not phonemically, as it is in French (e.g. mais [mɛ] vs. main [mɛ̃]).
Can versus can’t
In GA the only real difference between can and can’t is the vowel quality, and not (as is often assumed by students) whether or not the t is pronounced. In GA they are pronounced as [kən] (or [kn̩]) and kæ̃nʔ or [kæ̃ʔ]). Note that the negative form is nasalized. The only time that unreduced /ae/ is used in the positive form is when there is no chance of misinterpretation as in Yes, I can (do it), or phonetically, [jɛs – aɪ ˈkæn (…)]. i.e. a response to an assumption on the part of the first speaker. Because it is followed by a fortis obstruent, the vowel in the negative form is shorter than the vowel in positive form.