They all mean different things. I like using the Collins Cobuild online dictionary. collinsdictionary.com/dictionary/english-cobuild-learners I recommend you study the definitions, then create a sentence using each word and post your sentences here again. We can then give you feedback on how accurately you used the words and possible alternative uses.

Deduce would be to come to a conclusion, speculate would be to form a theory or hypothesis, and anticipate would be to expect or predict something.