How to make Debian package install dependencies?
If you install it via dpkg it won't work because dkpg doesn't know where to find additional dependencies. You could do it via apt-get if you build your own repo, but it's kind of time-consuming the first time (it's not difficult, just something "new" the first time that needs some time to be learnt).
On the other hand, and the solution you are probably looking for is gdebi (you may need to install it: apt-get install gdebi-core). It's a tool that checks the dependencies for a package and calls apt-get to fetch and install them, and then calls dpkg to install your package.
Per @textshell in this answer:
starting with apt 1.1 (available in Xenial (16.04), stretch)
apt installalso allows local files:sudo apt install ./foo-1.2.3.debSo much simpler and cleaner.
See the release announcment
This will also install dependencies, just like a normal apt install or apt-get install.