Some things I've learned over 40+ years and more than 100 owner-assist years are:
Keep a copy of the parts list in the plane and in your laptop so that that you can order a needed part while on the road. Ditto AD list.
Everything that happens in aviation MX is based on part numbers.
If you're working with a mechanic, ask him/her for a detailed show-and-tell as he works through the routine stuff so you can learn the procedures for timing mags, compression checks, r&r plugs and harness, how to check for exhaust leaks, etc. Also record the torgue values for everything that is normally removed or might come loose.
All MX isn't performed at home. If your plane has a known weak spot (such as alternator belt failure on old 210's) or common failure mode, learn how to replace and carry spare part and tools.
For example, I know that tailwheels are the achilles' heel of Cessna 180's and always carry an inflated spare along with bearings, axle, hardware (cotter pins) bottle jack and pad and ground-cloth/space-blanket/tarp in a toolbox (that also serves as a foot-stool and seat) in the bag compartment. I also carry a small bike pump with built-in pressure gage. Over the years I have changed a flat tire enough times to know I'll never travel without the spare. And if you break down on the road, finding a mechanic is easy but finding one with parts on hand is rare.
Carry some small tools in the cockpit. Trim screws fall out on every trip, usually replaceable with small Phillips. Many avionics failures can be fixed by simply "re-racking" the component by using a small Allen wrench to unlock and the unit to slide out a couple of inches then push back in and re-lock.
A can of WD-40, a length of clothesline or light rope, vice-grips, duct tape and electrical tape, a cheap volt-meter, a spare nav-light bulb, spark plug and a collection of sheet-metal screws, machine screws, bolt, nuts, washers, tie-wraps and safety wire can also be handy.
I carry a LED head-band light in the computer bag in addition to several flashlights in the plane. Parts and service manuals are available on the web, and can be stored in your lap-top.
A set of tie-down ropes and a couple of small chocks can be handy, especially for events (fly-ins and airshows) where availability is even worse than normal.
The stuff I carry weighs about 15# requires ~2 cubic feet. The plane flies a little better with some weight at aft CG limit, so it's a win-win to haul it around.
Another worthy assist is to make a list of components with part and serial numbers such as engine, airframe, mags, starter, generator, vacuum pump, ELT and anything else you can think of that may be subject to an AD. Time in service or time since overhaul or replacement would be great too. It will cut down on the first annual overhead for the new IA - stuff he won't have to research the second time.
If you're really ambitious you could look up the AD's online or go over an existing compliance list and find the relative compliance entries in the logbooks, marking them so the IA can locate them as he will initially need to verify each one. All of that takes time.
Of course, first you'd have to find an IA that will do an owner assist but some of these things will help even if you end up going into a shop.