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I notice that in some cases people skip the 's in the possessive case. But I cannot understand what rule they use.
For example:
Explain please how should I do it correctly?
The Saxon genitive (as we call the use of an apostrophe and the letter s to denote possession) is not skipped or omitted in the usages you cite.
Instead, the nouns attribute and pet are used as noun adjuncts or attributive nouns to modify the nouns which they precede.
Some other common examples are:
There is a Wikipedia article on the noun adjunct here. (Note that the article is in the process of being improved to reflect modern linguistic terminology; however, it does explain the concept succinctly.)
Your two examples do not show possessives, but instead show noun adjuncts – nouns which modify other nouns and change their meaning. Consider:
attribute declaration
an instance of an attribute being declared (by someone)attribute's declaration
a declaration made by an attributedeclaration of attributes
a thing (e.g. form/sheet) which declares attributes, or a declaration made by multiple attributes
pet cemetary
a cemetary in which pets are buriedcemetary of pets
a cemetary owned by pets, or made of pets as a material
There's no rule (that I'm aware of) that states how noun adjuncts are used or interpreted, and it tends to come down to convention (the widely-accepted meaning of a particular noun and set of adjuncts). For example, the following are all modifications of line but there is no consistency in meaning (other than that a length of some material is involved in some way):
clothes line
a string on which wet clothes are hung to drytelephone line
a wire down which a telephone signal is transmittedrailway line
a portion or length of track in the rail system
There isn't a correct way as such, it is more dependent on what you want to mean.
So "pets' cemetery" is a cemetery that is of pets. Pets' is the genitive, sometimes called the possessive, and it means that in some sense the cemetery belongs to the pets, although not necessarily in the way we usually imagine ownership.
However, "pet cemetery" is a cemetery involving pets. So instead of telling us about "ownership" of the cemetery, it talks about the cemetery itself. Pet in this instance is an attributive noun (also called a noun adjunct). It works a lot like an adjective.
So you use the genitive/possessive when you want to describe some kind of possession of or close association between two (or more) things. E.g.
You use an attributive noun when you want to describe one thing as an attribute of another. E.g.
