In the sentence "I need something to practice on", what type of word is on? It seems like an adverb, because it appears to be modiying the verb practice, but that just doesn't seem right to me for some reason.
It’s a preposition. You might be able to see that more easily if you recast the sentence as ‘I need something on which to practice’.
"On" is always a preposition unless it is part of a phrasal verb expression, as in "You're putting me on!". In this case, verb + preposition = phrasal verb. Phrasal verbs always have a different meaning than the "literal" meaning of the verb and it's preposition; in the aforementioned example, "putting...on" means "to joke, fool or deceive". It should be obvious that the speaker is not literally being put on something else.
For future questions of this nature, ask yourself this to find the answer: 1) Does the verb take on a different meaning because of the preposition? If it does, then the verb and preposition are a verbal phrase. If not, then the preposition is just that, and will have an object (if not expressed directly in the sentence, it will be an implied "which" or "what", depending on the context of the sentence.
It's a preposition all right.
It's just that the sentence structure is one that is discouraged by the purists, as in:
… a farmer will need more ground to apply the manure to.