How to I update Ralink 5390 adapter driver via terminal?

In Linux, most drivers (the ones that are open source) come with the kernel; so the packages that contains the driver are linux-image-generic and (possibly) linux-firmware (1).

You can check if it is up-to-date with

apt-cache policy linux-image-generic 
apt-cache policy linux-firmware

and updates should be automatic --- if not, the classical old sudo apt-get update; sudo apt-get dist-upgrade should work.

Notice that sometime there is a problem in upgrades that makes that the old kernel is retained; in that case use

apt-get install linux-generic

to update the kernel/firmware to the last available for your distribution.

If the device has a not open-source or a driver which is not in the official kernel, things are different, and are very device-dependent.

Footnotes:

(1) normal kernels. change -generic with -rt or -lowlatency if you have some fancy (audio workstation, real time) configuration.

Usually to upgrade your software and drivers on your system, the general method followed is

$ sudo apt-get update
$ sudo apt-get upgrade

Comment down if the problem still exists.