I'll give you some simple tips.
Always look for a chance to postion your sword in the right place in laning phase. If you get the sword in a good spot so it goes through your enemy, it does more damage (as you probably know.)
An easy way to sword in the right place for later is to go in for an early trade. First, you'd want to get your Grasp of the Undying stacks up for max damage. Then, you'd want to E through an enemy then Q for an easy trade. After you use all three Q's though, walk away as fast as you can. You wont win much trades with only your base autos.
From here, you got two choices of playstyles:
Now, that you got your sword behind your opponent, try to make the minions push in their favor so the wave goes close to your turrent. Shen's Q makes it easy to farm under tower, and if the enemy gets too close, your E can force tower aggro on them. This is a more passive playstyle. I use this against enemies I know I can't outduel (Ranged Top Laners, Fiora, Renekton, etc)
For a more aggresive laning phase, use you your Q once you can since the spirit sword is already behind the enemy. Then, if you aren't already close enough, E to them to force the trade. Now that the sword is on your side of the lane, all you have to do is E then Q onto the enemy to force more trades. Or, you can use Q for more effective farming. I use this playstyle against people I know I can duel (Tanks, Riven, etc)
Once you get six, you have to keep your ult in mind. Your ult helps you turn anyfight across the map. Keep a few things in mind about your ult:
Try to use it early game if you have teleport up. This'll prevent your own tower from falling while you help your team.
Low levels, your ult does not shield for much. Only ult if your teammate is 1/3 health or above if they are in a sustained fight. If your teammate is running away with low health, you could still ult them no matter how low they are.
Hope this helps M.M. I admire your dedication to Morde, so I am happy to help you learn Shenpai.