A few solutions could be:
- Color coding on shifter - Forward moving gears could be colored green while reverse is left white. Red wouldn't be ideal since that's so closely related to 'stop'. There are problems with this approach because does white clearly mean reverse? Would a user be looking at the gear when choosing them? Could the graphic on the gear selector be rubbed off?
- Icon indication on shifter - You could use individual icons for each gear with either an up arrow or down arrow depending on the direction. That would take up double the space since the arrows would probably be as large as the numbers. So, you could group the gears with one arrow for forward or reverse. The downside is using icons on the shifter is they would be obscured while the user was actually driving.
- Icon indicator on the dashboard - Up/down arrows on the display cluster would solve the obscuring of the indicators on the gear shifter and also the visual complexity the gear shifter solutions could cause. However, the problem here would be would the user know to look at the dashboard when choosing a gear? That information might be lost to the user when they most need it (learning how to drive) and only become apparent after they've learned how to drive.
This problem reminds me of two things, a quote and a similar situation in airplanes:
Everything should be made as simple as possible, but not simpler.
It's disputed who said that quote, but Einstein is the popular choice. The thought here is that at some point, making something more simple than it already is has the opposite effect. Adding indicators on the shifter or dashboard may make it seem more simple to drive, but in reality it makes it more difficult and isn't able to be a substitute for actual drivers training or a manual.
The Airplane Cockpit
There's a popular UX story that discusses how you could theoretically make a cockpit "simpler", but that simplicity wouldn't make an airplane easier to fly, in fact it would make it more difficult.
The complex set of gauges and controls is designed for a trained pilot, the pilot who is flying for endless hours during their career. Making the cockpit more simple would only benefit that pilot in the "learning how to fly" process that happens in their first hours and years. Once the system has been learned, simplicity for the new user makes the system more cluttered for the experienced one.
Your example would be aimed at helping the beginning driver, but much like the airplane cockpit, making the controls more simple would benefit a very small minority and confuse the more experienced ones.
Another thing to think about is would your user feel comfortable driving with that new information? Using a manual transmission has a much more difficult challenge for drivers that knowing which gear is for forward or reverse movement: using the clutch. Think about hopping into the simplified cockpit that's absolutely perfect for new, untrained pilots. Would you feel comfortable taking off and flying yourself and your family around? You need a bit of confidence in both of these situations to do them well. Training would be best, but a set of instructions could be a decent substitute.
So, to answer the question, training or a set of instructions are the best ways to get your new driver familiar with the workings of a manual transmission.