Working from home is not new to me. I worked remotely for five years for my current company. I even used dial-up connection for the first few months. I would go to an internet cafe if I needed to send larger documents. The conditions to work from home nowadays is much better and it also works even if you're just using mobile connection.
Some countries have also opted to close schools for the meantime. Learning continues for students even with schools closed. I see my Japanese teacher friends share how they have been managing. Aside from continuing their lessons, they are also required to check on all their students every day.
Here's what I use when I work remotely (and I'll put some notes at the end on what you can use if you're a teacher/student):
Hardware - I use a Chromebook. For work I use whatever is issued to me. For personal use I still use my Samsung Chromebook (circa 2014). I do everything anyway on the cloud and don't use fancy expensive apps. (more about Chromebooks here)
Communication - Your Gmail account is all you need. It has everything I need to communicate. I use Gmail for sending emails/emailing documents with attachments. Google Hangout for video conferencing and calling (I use it to call my Mom on her landline). If you have a company then you should use GSuite for Business to make it easy for you to keep your data within your company.
Collaboration - Google Drive is your best friend when creating documents (Google Docs/Spreadsheets), presentations (Google Slides) and it makes it so easy to edit a document at the same time as your colleagues.
Productivity - My meetings are most of the time done with colleagues from other countries. I go around the globe everyday. Usually start in the US/Australia early in the morning, then I progress to North Asia countries, then Southeast Asia and then Europe by late afternoon. Sometimes Latin America too. Managing timezones and setting meetings has been easy with Google Calendar. When you set-up a meeting, add who you want to invite and add a link for a Google Hangout. When it's time for your meeting just join the Hangout link from the Calendar invite. Then to keep tabs with things you need to do, you can opt to take notes using Google Keep (which you can also easily share with someone else).
For Schools - I know a lot of schools have just been using personal Gmail accounts, but it's much better if you use GSuite for Education so you can control better the platform your teachers and students use. It's a free tool that Google provides for schools (just sign up here). If you need help to set up your account you can contact any of the Google for Education partners.
For Teachers - My teacher friends absolutely love Google Classroom. This makes it very easy for them to manage their class. You can easily set-up homework/assignment for your students and even run quizzes. And the best thing about it is you can easily record grades and share updates for parents. To run activities for your students, you can use Google Jamboard and watch them contribute live during the session. If it's too much for you, you can also just use Google Docs. [Google Classroom Tutorials, Forms tutorials] *And yes you can also use Google Classroom if you just have a consumer Gmail account.
If you want to run live lessons, you can opt to do a class using Google Meets. If your school is using GSuite for Education, you can host up to 100 students in your Google Meets session (and up to 250 until July 1, 2020). If you're just using a consumer Gmail account then you can host only up to 25 participants. It is best to put your students in a Google Group so you can just use the group email address when adding a Calendar invite.
When hosting your hangout you can also easily share your screen. Depending on your connectivity you can also show videos to your students. If you feel that connectivity is an issue you can ask everyone to just turn off their video and keep it as a voice call. I oftentimes join meetings on my phone even when I'm traveling. If you're hosting a larger class, you can also use Youtube Live.
You may be worried that there may be a lot of things to learn. Using the tools I mentioned above are tools you are likely already using during your personal time. Just try and explore, it's easy to learn :)
More resources you can check out -
Google initiative for school closures
Google for Education YouTube channel (demo videos available here!)
GEG Program YouTube channel (teacher made demo videos, Mandarin/Cantonese/Japanese videos now available)
What's the difference between Google Meets and Google Hangouts