Toren

I would follow the same approach as fuzzy. For me, it's important to be learning both the theory and the applications at the same time. I generally start with theory but just the surface level stuff. Then, I try to make a rudimentary version of it work. Probably will encounter tons of roadblocks along the way, so I would dig deeper into the theory whenever I get stuck. When I have a basic working model, I can go back and implement more details, generalize it more etc. 
It's helpful to do this with someone who knows what they are doing. You don't necessarily need their direct supervision, but guidance from them can really help. Also, eventually, you will have a complete model/product/etc. and it would be really helpful to have an expert take a look and try to poke holes in it. Since at this stage, you might not know the theory deep enough to understand caveats, so consulting an expert that knows about the main traps/pitfalls is helpful. The suggestion to join an existing project with others who are already using the method is a great one, if that opportunity is available!

It depends on the person, but for me, the best strategy has been to join existing projects with people who are more knowledgeable than me and get some hands-on experience in a setting that also allowed me to ask theory and technical questions as needed, and where someone else could make sure that I wasn't going off in very wrong directions. I can get lost in theory, but application is easier to make sense of, especially in a context where I can't mess anything up too badly because I'm not doing the whole thing alone. Over time I also ask the theory questions and I can make connections between the actions and particular choices I've made and the reasons behind them. That's generally worked best for me, after some initial reading to get enough background to situate whatever I'm learning in some basic theory.

If a grad student is hosting you then you'll either be on the couch, an air mattress, or a cot.  It probably isn't the norm for them to have a proper guest room.  Your mode of transportation will likely influence what is provided for you.  Last year I had to fly everywhere so the students that hosted me knew I couldn't just lug blankets and pillows on board with my carry on and had all of that waiting for me.  If I had been able to drive I would have brought my own bedding.
Some do and some do not.  If you do this then keep whatever you give around $5 so it is very clear that it is just a thank you and nothing more.  You could always just do a thank you card with a personalized note.

Potentially really dumb question - but when grad students provide housing, does this mean we'll be sleeping on their couch or something? Should we bring extra blankets or pillows just in case? 

Is a suit overkill for guys during interviews ? Anyone willing to share what other males have worn to interviews ?