I've worked remotely for the past four years now and the skills that have helped me thrive the most is being an effective communicator and resourceful. For me, I've found that working with other folks in different locations and different time zones, asynchronous communication is key. As such I had to be good at writing up emails that conveyed my thoughts and needs. It's also a good skill to exhaust all your options by looking into solutions you find on the Internet first before asking your colleagues.
Being on an engineering team, we used JIRA to track tasks and bugs. As such my questions had to be clear or there would be several cycles in trying to make sure questions were clearly understood on both ends. I also was relentless with making sure that others communicated clearly and didn't make assumptions such as something being low hanging fruits on JIRA. What this yielded in was better expectations and smoother workflows between coworkers.
Being able to write documentation was important as well. As knowledge transfer had to happen in many instances when new folks joined or a project was handed off. Being able to write documentation isn't easy. Since as someone who has a lot of area knowledge you make assumptions and it can be really confusing for others. I've found that being able to take feedback through peer reviews was helpful. Especially if the person reviewing fit into the audience the documentation was intended for.
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