Find a good mechanic that is close and allows owner assisted annuals that either knows Mooney specifics or is willing to learn. Mooney maintenance and parts manuals are necessary and very helpful. If you do not already own a set get them. MS is a great resource to locate and find Mooney specific issues to look for during an annual or pre-buy.
Engine and controls - common between all aircraft and any good mechanic / IA will understand and is not an issue
Airframe inspection - cleaning, lubrication, looking for cracks, corrosion, control linkages, rod end wear similar on all airframes
Gear rigging - Mooney specific and need Mooney specific tools and manuals (gear tools)
Gear shock discs - Mooney specific and need Mooney specific tools and manuals (gear tools)
Control rigging - Mooney specific and need Mooney specific tools and manuals (travel boards). Once verified on your first annual if nothing was changed little need to check every annual unless you notice something different when flying.
I'm sure I missed something and this is not intended to be a complete list of things done on an annual. However, these are the big groups of activities that I see when assisting with the annual.
Get you hands dirty.