The basic repair skills while on the road is how to repair/replace a flat tire...if you're using a tube in a tire system.
This includes how to remove the wheel, remove one side of the tire, remove the tube, replace the tube, inflate the tube once in the tire, put the wheel back on the bike and having the bike in a good gear to resume your ride.
A properly maintained and adjusted bike doesn't often need any other road side service...unless something goes wrong.
General maintenance skills for in the 'shop' should be how to CLEAN and lube your chain...adding layer upon layer of lube is a nasty practice. Cleaning your bike and wheels, inspecting the bike's parts...which should always be done while cleaning the bike. Checking the gear, generally the rear derailleur needs the most attention as it does the most work. How to clean your brakes and brake surfaces.
These are the basics and generally don't require specific tools...other than routine chain stretch checking with is made easier with a specific tool which, fortunately, doesn't cost a lot of money.
You could start by asking in a local bike shop of good repute. Or you can ask someone you ride with whose bike always looks the cleanest, has no or very few problems during group rides, etc...Don't expect something for nothing and if the person is willing pay them for their time, if they refuse, gift them with something nice. While classes are useful I'd prefer a one on one working with my bike. I'd ask if someone with the necessary skills would be interested in teaching me basic/routine cleaning, adjustment and maintenance of my bike. If someone is interested, pay them...don't expect something for nothing. The skills you learn will last for the rest of your life, make servicing and maintaining your bike easier and you can pass it along to a friend, etc...at least the basics.
General tools all 'riders' should have include a set of metric Allen wrenches, chain stretch checking tool, tire levers, floor pump, chain cleaning kit ( I prefer the Park chain cleaner and Muc Off, they will do a great job and the chain stays on the bike, a torque wrench...most people over tighten which is not good for carbon frames and parts, a work stand...while not a MUST HAVE I consider it a must have and one can be purchased at a reasonable price...it may not be fancy or the easiest to use but worth every penny in the long term, lubes for the chain and fiddly bits, cleaning and polishing materials, etc which are usually the rider's/mechanics favorites/preferred bit of kit.
These are the basics for routine servicing and maintenance and doing it on a weekly basis will make you more proficient over time.