Idioms involve collocation of a special kind. Consider, for instance, kick the bucket, fly off the handle, spill the beans, red herring. For here we not only have the collocation of kick and the bucket, but also the fact that the meaning of the resultant combination is opaque - it is not related to the meaning of the individual words, but is sometimes (though not always) nearer to the meaning of a single word (thus kick the bucket equals die).
Even where an idiom is semantically like a single word it does not function like one. Thus we will not have a past tense * kick-the-bucketed. Instead, it functions to some degree as a normal sequence of grammatical words, so that the past tense form is kicked the bucket. But there are a great number of grammatical restrictions. A large number of idioms contain a verb and a noun, but although the verb may be placed in the past tense, the number of the noun can never be changed. We have s pilled the beans, but not * spill the bean and equally there is no *fly off the handles, *kick the buckets, *put on good faces, *blow one's tops, etc. Similarly, with red herring the noun may be plural, but the adjective cannot be comparative (the -er form). Thus we find red herrings but not *redder herring.
There are also plenty of syntactic restrictions. Some idioms have passives, but others do not. The law was laid down and The beans have been spilled are all right (though some may question the latter), but *The bucket was kicked is not. But in no case could we say It was the - (beans that were spilled, law that was laid down, bucket that was kicked, etc.). The restrictions vary from idiom to idiom. Some are more restricted or 'frozen' than others.
A very common type of idiom in English is what is usually called the 'phrasal verb', the combination of verb plus adverb of the kind make up, give in, put down. The meaning of these combinations cannot be predicted from the individual verb and adverb and in many cases there is a single verb with the same or a very close meaning - invent, yield, quell. Not all combinations of this kind are idiomatic, of course. Put down has a literal sense too and there are many others that are both idiomatic and not, e. g. take in as in The conjuror took the audience in, The woman took the homeless children in. There are even degrees of idiomaticity since one can make up a story, make up a fire or make up one's face. Moreover, it is nof only sequences of verb plus adverb that may be idiomatic. There are also sequences of verb plus preposition, such as look after and go for, and sequences of verb, adverb and preposition, such as put up with ('tolerate') or do away with ('kill').
There are also what we may call partial idioms, where one of the words has its usual meaning, the other has a meaning that is peculiar to the particular sequence. Thus red hair refers to hair, but not hair that is red in strict colour terms. Comedians have fun with partial idioms of this kind, e. g. when instructed to make a bed they bring out a set of carpenter's tools. An interesting set involves the-word white, for white coffee is brown in colour, white wine is usually yellow, and white people are pink. Yet, white is, perhaps, idiomatic only to some degree - it could be interpreted 'the lightest in colour of that usually to be found'. Not surprisingly black is used as its antonym for coffee and people (though again neither are black in colour terms), yet it is not used for wine. Thus it can be seen that even partial idiomaticity can be a matter of degree and may in some cases be little more than a matter of collocational restriction. On a more comic level there is partial idiomaticity in raining cats and dogs (in Welsh it rains old women and sticks!).
What is and what is not an idiom is, then often a matter of degree. It is very difficult, moreover, to decide whether a word or a sequence of words is opaque. We could, perhaps, define idioms in terms of non-equivalence in other languages, so that kick the bucket, red herring, etc., are idioms because they cannot be directly translated into French or German. But this will not really work. The French for nurse is garde-malade, but while this cannot be directly translated into English it is quite transparent, obviously meaning someone who looks after the sick. On the ofher hand, look after seems quite idiomatic, yet it can be quite directly translated into Welsh (edrych ar o1).