Time and patienceI took me a while to figure out to push slowly on the right (rear) so I wasn't skipping multiple gears.. the left (front) was less touchy since it was pretty much switching from just one or the other.
You can also check to see if the cables are adjusted properly so that the derailleurs can shift through the whole range (a stand is helpful for this, but if not, a friend can hold the rear end up for you). There may or may not be limit screws on the derailleurs, and you may or may not need to adjust the cables (and your bike may or may not have barrel adjusters, so you may need to do it the hard way).
ETA, for anyone wondering, stem shifters look like so:
They were more common in the 70's and 80's.