You'd be surprised by what can be achieved by just having Slack. The best parts of IRC and email, put together. Searchable. Persistent communication changes companies. My current employer is only running part-remote, but we actively move important conversations to slack, because if nothing else, we can go back to them later.
When sharing actual screens is necessary, there's ScreenHero, which is very useful for pair programming and such.
Now, I think it's important to have at least some video chat every day, if just so that we can keep up with the emotional state of our coworkers. Over the years, I've preemptively fixed many team dynamics problems by paying attention to people's emotions. If Joe is sad today, maybe I can help with whatever the problem is, or I can at least make sure he isn't pressured too much. If you do most of your talk by text, it's far harder to pick up on those things. If there's some rotating pair programming going on, those things can be handled better.
We do use Slack and it certainly helps. However, we invariably find that there is a certain inertia to reach out via video among some devs or wait until the person is in office to hash out a problem. It may just be because we don't have anyone 100% remote on the team and hence expectations aren't set. Also, in an open office plan, talking over video at your desk can becoming annoying to the person sitting next to you, which means grabbing a conf room. I'm just saying it depends on the personality of the developer in how she/he handles working with a remote worker.
When sharing actual screens is necessary, there's ScreenHero, which is very useful for pair programming and such.
Now, I think it's important to have at least some video chat every day, if just so that we can keep up with the emotional state of our coworkers. Over the years, I've preemptively fixed many team dynamics problems by paying attention to people's emotions. If Joe is sad today, maybe I can help with whatever the problem is, or I can at least make sure he isn't pressured too much. If you do most of your talk by text, it's far harder to pick up on those things. If there's some rotating pair programming going on, those things can be handled better.