I have flexible work hours and can be available any time between 7:00am and 9:00pm EST. I prefer Skype or Google Hangout communication because it's the closest alternative to face-to-face, but a phone call works fine as well. I usually use email as a follow up recap for a call or video chat (e.g. "Here's what we discussed today on the phone, let me know if anything is missing or needs an update") or for quick questions, but I like to avoid long email chains because I think they are unproductive after a point and start to waste time, and waste money for both parties.
If I bill hourly, I never charge for time spent on research or learning your system unless it's agreed upon beforehand, at which point I would work with you to set a maximum time to bill for this kind of overhead. Otherwise, I'm open to different types of contracts.