You are right. At the basic end of things you do the most simple thing and use 2 bytes instead of 1.
As a learner it is very instructive to do some binary with a pencil and paper to see how it all works.
put the column weights in a row at the top and then put 16 zero's underneath.
Then start some rows with ones in various places and write the decimal value against the rows
draw vertical lines in between each group of 8 columns so you can see the byte boundary easy
I have taught a number of people using this method and people seem to pick things like shifting up easy
this way too.