The command syntax for the vast majority of games is:
verb_phrase [noun_phrase] [[preposition] [noun_phrase]]
The verb phrase is a verb (e.g. LOOK) or a verb followed by a preposition (e.g. LOOK AT).
The first noun phrase is usually the direct object. This may include a definite or indefinite article (A, AN, SOME, THE), but most parsers will strip this off in most circumstances. This may optionally be followed by one or more adjectives (e.g. BIG, BLUE) and one or more nouns (e.g. BALL). The looser parsers (such as Inform 6 and 7) will allow the adjectives and nouns to occur in any order and you can even omit the noun and use only an adjective. Hence article, adjective(s) and noun(s) are all optional, but you must provide at least one adjective or noun to uniquely identify the object you’re referring to.
If there are multiple objects in scope (usually meaning able to be seen and/or able to be touched, depending on the verb being used), then you need to provide enough information to identify the object you want or you’ll get a disambiguation question. For example, if there’s a green ball and a blue ball in scope and you say GET BALL, the parser will ask you which one you mean, the green ball or the blue ball and you can respond with BLUE or BLUE BALL without a verb.
The second noun phrase is usually the indirect object and it abides by the same rules as the first noun phrase re article, adjective(s) and noun(s). The preposition separates the direct object and the indirect object. If the preposition is omitted, then the direct and indirect objects are swapped. For example, GIVE AXE TO DWARF and GIVE DWARF AXE mean exactly the same thing, where AXE is the direct object and DWARF is the indirect object.
These are the basics that apply to pretty much every parser-based game and every authoring language. There are more advanced features like referring to all objects using ALL or EVERYTHING, use of multiple objects using AND, excluding certain objects using BUT or EXCEPT, and stringing multiple commands together, but new players don’t need to know all that stuff.
Regarding common verbs, these are pretty much standardised, but the range of verbs varies slightly from language to language, even Inform 6 standard library, Inform 6 PunyInform library and Inform 7 have a slightly different set of default verbs and default grammar.
Each game will be customised by the author to add or delete verbs and modify the grammar so that it all makes more sense within the context of that particular game. Similarly, the default responses to the default verbs can be customised.