1) Good communication (as many others have mentioned) - team members were always on chat (campfire->slack) while working. We also had semi-regular weekly video chats where we talked about what was going on. Video was nice because it helped to put faces to the people you were working with.
2) Don't focus on work 100% of the time - just like non-remote offices, people need time where they can chat about non-work related things, like games, home life, funny cat pictures, etc. Talking about these things helps create bonds beyond work, and improves the team imo.
3) Meet in person occasionally - the team all met once a year in person. Yes it can be a little awkward initially, but it also helps to further cement that there is a real person behind the chat.