As a long time Slack user, I've found that the following tips can help you make your team's communications clearer and more effective.
1. Don't lose the sense of fun
Slack is designed to be a fun - joyful even - tool to use, and the main reason that people adopt it so well is that it doesn't "feel" like enterprise software. Given the space, your staff will use it as a common area and express themselves as humans - and as it becomes a vehicle for more than status checkins and robotic corporate messaging, you'll see much more value from it.
2. Keep as much as possible in open channels One of the biggest advantages of a system like Slack is that it gives a time-series, conversational record of what's gone on. This is incredibly useful for everything from catching up after your holidays, to giving context to new staff members, to internal affairs-style security auditing.
Most of this advantage evaporates straight away if your team spends too much time in private channels. It's an anti-pattern; encourage them to communicate in the open as much as possible (and if they won't - ask yourself what it is about your company culture that makes them reluctant)
3. Have a channel naming convention
As the number of channels grows it can be hard to see what's what, and what's important. Establish a naming convention early on. Prefixing "official" channels with "-" is a good one - it'll cause Slack to place them at the top of the channel list so they can be spotted easily.
4. Encourage people to use the Status feature
Presence is a powerful feature, as it gives real-world context to people's usage of the app. Use custom emojis representing your office locations to tell you where people are, or the "Pal Tree" emoji to make it clear you're on holiday.
And set yourself to Away or DnD when you need to calm down those notifications even more!
5. Train people, just a bit
Slack is easy and intuitive - but online group chat (as opposed to, say, SMS) is still alien to many folks.
In particular - show people how to control their notifications on all their devices - it'll stop a raft of complaints.
Bonus tip - make it searchable
Slack includes a reasonable search facility - but if you're also using other online tools like Google Drive, Trello, GitHub or even email, it's a hassle to have to go into the UI of each tool and search when you're trying to find that particular customer message you remember receiving.
If this is a problem that feels familiar then have a look at CTX and see if a single, secure search over all your tools would make your life easier or save your team time.