I have just started studying Phonology and I find a problem while dealing with Syllables. I read that nuclei are not only vowels, but they could be also liquids (l - r) or nasals (n - m - ng). But what I already learned when I studied Articulatory Phonetics is that Nasals and Liquids are [ +Consonantal , - Syllabic ].
Could you please explain to me with examples how a liquid/nasal become a nucleus of a syllable?
First off, phonetics is not about features, though often in introductory classes if you don't have separate courses on phonetics and phonology, phonetics gets lumped together with phonology. Second, it is simply wrong to say that liquids and nasals are [+cons,-syll]. The misstatement comes from confusing the most common properties of a system with the inherent properties of the system. Liquids and nasals are [+cons,+son] and if you want to distinguish syllabic versus non-syllabic liquids / nasals (the latter are more common), you can employ [syllabic] to do that – syllabic liquids/nasals are [+cons,+son,+syl] and nonsyllabic liquids are [+cons,+son,-syl]. That assumes the classical SPE feature system, and in fact syllabic was one of the first features to be disposed of in the 70's. Textbooks may use the SPE system because it does represent the last standard for representation, but there are many current theories of representation, and none of them employ a feature [syllabic]. There are many different accounts of the difference, virtually all of which rely on some prosodic object such as a mora, V-slot, or nuclearly prespecified X-slot (there is also a non-standard redefinition of [consonantal] where glides are [+consonantal] and corresponding vowels are [-consonantal], but as far as I know that has not been applied to the difference between syllabic and non-syllabic consonants.
It is a somewhat open question how "deeply" a syllabic / non-syllabic distinction is needed. There has always been a strong urge to get rid of the distinction, because most of the time you can predict where things are syllabic. In fact, if you also have syllables (which we don't always have), then you can always predict syllabicity. Problematic cases like the Swahili minimal pair mbuni "ostrich", m̩buni "coffee tree" become non-problematic if you include syllable structure – mbu.ni vs m̩.bu.ni. As it happens, the distinction in Swahili is more superficial and there is no need to admit an underlying contrast in syllabicity types for nasals – it can be predicted, once you have the rule system sorted out. For theories that posit moraicity as the bearer of the concept "syllabic", there isn't much hope of predicting "syllabicness" because moraicity is a fairly fundamental phonemic property (since it is also how you express long versus short).
There is no general answer to the question of how liquids and nasals become syllabic: there are many answers, and it just depends on the facts of the language. In English, it mostly has to do with unstressed syllables having əC where C is a sonorant. In many languages it has to do with extraneous consonants that can't be syllabified around a vowel but where there is a sonorant that can fill the bill (Sanskrit, for example). A number of languages of West Africa have CR̩V syllables with syllabic pre-vocalic consonants, and these often derive from disyllables (*pila) which lose a vowel (→ [pl̩a]).
Liquids and nasals can sometimes be syllabic as well. (In fact, in Berber, even stops can be syllabic sometimes.) The more precise IPA symbols for these syllabic consonants add a vertical dot underneath the letter, e.g. [sɪləbl̩].
As for how that happens, it's one of the strategies that a language can employ to syllabify stray consonants. I'll illustrate from a derivational perspective (as I assume you haven't gotten to optimality yet). English doesn't allow [bl] to be a coda, as it violates sonority. So when you try to syllabify /sɪləbl/, after the first pass you get sɪ.ləb.l with a stray [l]. So the English system tries to fix this by turning the [l] syllabic, into [l̩], and subsequently assigning a sigma to the newly syllabic consonant. Then the [b] gets re-assigned as the onset of the brand-new syllable, and eventually you end up with [sɪ.lə.bl̩].
You can compare this with the French system, which has no problem with [tabl].
P.S. Your curriculum sounds slightly odd... distinctive features are a phonological theory rather than a phonetic one.
Here is how to say d + l as one syllable. First, say d + schwa + l, where the schwa is the syllabic sound of the syllable. The tongue tip must leave the alveolar ridge for the schwa. Now, say the same thing, but this time, keep the tongue tip in contact with the alveolar ridge. That's it -- you've just said a syllabic l after the d.
You may doubt that there is a real phonological distinction between the version with schwa and without it. Here is a phonological argument that there must be a distinction. The typical American English pronunciation of "little" has a d for the "tt". This is because of the intervocalic flapping of t. When the t flaps, it becomes sonorant, and sonorants are voiced in voiced surroundings, so the flap voices.
We only get flapping before vowels, so we know that t is not immediately followed by l when the process of flapping applies. There must be a vowel (a schwa) between the t and l of "little".
But how can we account for the pronunciation with d (rather than flap)? A flap has only a brief contact with the alveolar ridge, so if the schwa after the t which made it possible to flap the t now disappears, the flap has to revert to the corresponding obstruent d. This is a contact phenomenon.
So, we begin with phonemic t + schwa + l, then we get flap + schwa + l, then after schwa is lost, we wind up with d + syllabic l. There is no schwa between the d and the l.
Similarly, we know there is no schwa between glottal stop and n in a word like "rotten" with glottal stop for "tt", because t does not change to glottal stop before a vowel in American English.
