I know in general terms how to use "very much" but since my students started making specific questions and writing sentences like the one above I got very confused (I'm brazilian, and I just started working as an English Teacher).
I would say that the sentence would sound better if it was "I like to play volleyball on weekends very much", but I want to understand what positions it could be placed and how it would change the sentence's meaning.
As John says, "very much" modifies a verb phrase. It means the same as the more casual "a lot" or "a whole lot". It's most natural position is after the verb phrase that it modifies, just like "a lot", but unlike "a lot", it can also go before the verb phrase that it modifies or after the main verb of that phrase.
When "very much" modifies a preceding complement construction, there is often a distressing ambiguity about whether it modifies the main verb phrase or the complement verb phrase: "I prefer not to eat snails very much" could mean either that your preference for not eating snails is extreme, or that snails are okay if indulged in only occasionally. That ambiguity is resolved by moving "very much" to a position either immediately before or immediately after "prefer", because then "very much" can only modify the entire verb phrase with "prefer".
On the other hand, "a lot" cannot be disambiguated in this way, since it has to go after the verb phrase it modifies. I think that this sort of disambiguation is mainly what "very much" is useful for, at least in casual conversation.
When "very much" comes before the verb phrase it modifies, it follows auxiliary verbs or other adverbs:
I have always very much preferred fish.
??I have very much always preferred fish.
*I very much have always preferred fish.
When you use a verb as a transitive verb, the phrase "very much" usually goes after the object; we should not use it after the verb. So you usually say:
I like to play volleyball very much on weekends.
However, it's also correct if you use the "very much" at the end of the sentence or before the verb as follows:
I like to play volleyball on weekends very much.
I very much like to play volleyball on weekends.
I think it's unidiomatic to use the "very much" between the verb and the object such as:
I like very much to play volleyball on weekends. The infinitive phrase "to play football on weekends" is functioning as a direct object in the sentence.
Adverbs are funny things--often, they can appear anywhere in a sentence and not affect meaning. Grammatically, there is no difference between "I very much like to do X," "I like very much to do X...," and "I like to do X...very much," though idiomatically, the first choice seems to me the best. Another issue worth addressing with your students, though, is when such adverbs should be used at all. For example, you might ask your students why they don't instead say "I love to play volleyball on weekends." Otherwise, someone might say, "I really love to play volleyball"--but does this convey more information than "I love to play volleyball," or does it simply add a word?
I have to say I agree with Matt. I teach children around the world, and while using 'very much' is correct, I explain to my students that we don't often hear "I very much like..." or "I like ... very much." In most casual conversations, we say "I really like..."
In fact, I just had that conversation with my student today when she told me that her mom "very much likes burritos."
"I very much like to play volleyball..." is a rather formal, but completely correct, use of that phrase.
In common speech, I would suggest using other words, such as "I really like to play..."
But that may contribute to lessening our beautiful language; I don't know ;)
