If you have questions about the direction of your research (e.g., x or y method), how willing is your supervisor to discuss the alternatives? Do they talk through ideas with you, or are you left to figure everything out on your own?

I think this really depends on what stage you are at. In the earlier setting up phase they were very willing to discuss other methods and hypotheses as these related to the literature searching and subsequent justification of my approach. Later on in the PhD journey, I found that much more was down to me to direct and specify the final approach as this is the time that you are becoming an independent researcher. Our discussions at that point were more about what I had found and how I had interpreted this way, along with my follow-up direction. Obviously, they would add advice/comment as necessary!

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As dunni73 says it depends on the stage you are at in yor PhD, also on your supervisor and the project. I had quite a wide project scope so in effect I could take the project almost anywhere I wanted. Other people I know had a very well defined project and had to follow a set path.

As regards methods etc my supervisor was good at discussing though things like that if he knew the methods, if he didn't we would discuss our opinions on something if I wasn't getting somewhere with a method he would help me figure out why.