I probably don't do it as well as I could, and I am trying to minimize my past mistakes of analysis paralysis followed by massive scope creep, hoping to avoid being a decade and five figures into the project, still nowhere near done, and finding that the goals I set ten years ago are not particularly relevant anymore!
If the project isn't running, the first steps are a careful check over and troubleshooting. If it is running, a careful check over and cautious test driving are the first steps. Tires, brakes, fueling, battery/electrical/wiring are the highest priority. A basic check and replacement of all fluids is often called for, along with dealing with any fluid leaks. Suspension/chassis/steering wear is not too far behind, and the rest can be tackled once it is safely running and riding/driving.
From there, I try to assess what bothers me about the vehicle, or what I wish it would do better, and use that to guide my planning for future repairs and upgrades.
I like doing internet research, but I take most it with a grain of saltshaker. The tough part about it is that Joe Q Internet might have a completely different set of priorities than me. There can be really useful tips like, "XYZ ground is known to be dodgy and can result in hard-to-diagnose issues" and then there is also the dubious advice like "you gotta get XYZ brand/model of performance part, it is the best" or "ZOMG, check out this crazy DIY performance/upgrade hack!" that gets passed around until it approaches fact, but isn't backed up by much if any objective testing, and may have berkeley all to do with my personal goals for the vehicle. I try to use internet research to add items to check to my list, and to help me narrow down upgrade options to research further.
I love finding stock parts from another vehicle that provide an upgrade for my application, and will spend hours on the internet chasing down possible parts-bin cross-compatibility.
Finally, I *try* to take a systems approach to things. I may not always do it really well, but if I am happy with moderate-grip tires, I don't need to go nuts with huge brakes and heim joints and hard bushings everywhere in the suspension. If my engine tuning plans are aimed somewhere north of the moon, I better also consider driveline upgrades, bigger tires, chassis reinforcement, etc.