Alex - I learned Spanish completely alone, without any classes. For me the most useful thing was reading, I used to (try to) read the newspaper, but children's books may be better. Be prepared not to understand much at first, be satisfied with understanding the gist and guessing the meaning of a few words. Your dictionary will come in handy here but don't be tempted to use it for every word you don't understand. It's good to use tapes or CDs from the beginning so you can work on your pronunciation - the earlier you work on this the better.
As for learning vocab, the best way is NOT to write a list with the translation. Try pictures, diagrams, example sentences (with real examples relevent to you), recording it onto a tape or dictaphone, whatever works for you. Try making your own "phrase book", a different topic for each page and you can add to it as you meet new words and phrases. Rember it's often much more useful to learn a whole phrase than the seperate words. Writing short stories with new vocab is also very helpful, if the story is really stupid even better, it will help you remember! Oh, and buy a learner's dictionary - that is not a translation dictionary but one written in Spanish for learners of Spanish.
I agree with your granpa, it's best not to translate if you can help it. However don't worry if you're thinking in English, this is normal, you'll start thinking in the new language in time.
Hope that helps.