Alrighty, here's when my linguistics comes in handy

A
phrase is basically a string of words.
A
sentence starts with a capital and ends with a full stop, and
contains (one or more) clauses. The basic structure is SVO (subject verb object), or, using phrases, NP VP.
A
clause is a group of phrases containing a verb, pretty much.
Each phrase has a 'head' word, i.e. one that gives the phrase the most meaning. There are various tests to see what the head word is. It determines what type of phrase it is (but generally, this is when you have a sentence, so it's slightly irrelevant).
Your first two phrases are actually
noun phrases (NP). You're concentrating too much on the embedded adjective phrase (AdjP). In English, various things can modify nouns, AdjP being one of them. When looking for a noun phrase, try changing the premodifiers (in these cases, AdjP) and see if it changes the actual object. Or try to change the noun itself - if that gives a different meaning to the phrase, then it'll be a NP.
For example:
those dirty old smelly sneakers --> Those pretty unused newly bought sneakers (you can change the AdjP without changing 'sneakers', the head word)
those dirty old smelly sneakers --> Those dirty old smelly men (different meaning completely, the noun is the head word)
In the later example of "few people of learning", "of learning" is a prepositional phrase (PP) postmodifying "people".
Don't forget that pronouns and proper names can also be NP.
If it's just a string of adjectives with a possible adverb chucked in there it'll be an
AdjP. They're pretty easy to find.
For example:
pink and purple = AdjP
BUT
pink and purple bathing caps = NP
As soon as AdjP describe something, they aren't the head of the phrase.
PP are generally (I wouldn't know if it was all, but close to all, I think) constructed from a preposition and a NP. You have to be good with your prepositions for these.
"In the galley" is a PP - The preposition "in" and the NP "the galley".
Verb phrases (VP) are also pretty easy. Look for a verb

But beware, VP do not only consist of the verb. They also consist of whatever the verb modifies. You can see NP, AdvP, PP after them.
For example:
"She pounded the pavement" is a sentence. (NP + VP)
"pounded the pavement" is a VP.
"the pavement" is a NP.
Lastly,
adverb phrases (AdvP). For this, like PP, you have to know your adverbs. Generally it's fine - look for the '-ly' morpheme. But there are a few pesky adverbs which you don't think are adverbs, same as prepositions. To discern whether it's an AdvP, try moving it around in a sentence. It should fit in in another slot in the sentence.
For example:
the sentence "eventually she arrived" is AdvP NP VP.
Why?
"she arrived" = NP VP.
But you could also put in "eventually in two other spots.
"she eventually arrived"
"she arrived eventually"
Therefore "eventually" = AdvP. (But "eventually she arrived" = sentence)
[Edit: whoops, forgot predicate etc.]
The NP VP of the sentence pretty much corresponds to Predicator Predicate. NP=Subject=Predicator; VP=Everything else=Predicate. Predicate also is like the VP; it includes everything after the verb.
A complement is a special type of thing which comes after copula verbs. These are the verbs like "be", "become", "appear", "seem" etc. They describe a state rather than an event. The complement is the descriptor, generally a AdjP, but can be other things.
For example (complement=italic):
I am
happy.
I'm a
student.
He seems
sad.
Vanessa appears
to be studying.
My dad's becoming
deaf.
She's
glowing.
This might be a bit hard to understand, sometimes I don't make sense ==;;
But basically, you know what a sentence looks like. If the string of words acts like a sentence (i.e. try to put into context), it will be. Phrases don't seem like complete sentences. REMEMBER to locate what the head word is first. Everything will come after.
I'll give you a quick clue: there are no AdjP or AdvP and quite a lot of them are sentences.
Good luck with your outcome! Be sure to ask any questions if you still don't understand
