Get to Know the Culture of the Organization
After you're hired, it doesn't mean all that's left is heads-down programming. You should continue learning as much as you can about the organization. This will help you work smarter as well as build trust with your counterparts. Most importantly, be proactive in figuring out how your client or manager operates and build off of their style of communication.
That goes for non-verbal communication, too. If team members are expected to be available via video during their shift, make sure you're available during yours. If they sing happy birthday to each other via Google Chat, then join in! If they send e-cards, do the same.
Be Complete When Asking or Answering Questions
Many times, I see emails or hear about issues where the deliverer fails to provide complete context. Without enough background, issues simply can't be acted on. When you're a remote freelancer, you can create considerable goodwill by being complete, especially if you're working a schedule that is different from HQ's or other programmers'. That way, your contacts will always have the information they need and can address things in a timely fashion, even if you're not online.
Whenever possible, include screenshots, documents, and message threads. Err on the side of over-communication rather than assuming that recipients have all the information they need.