Ive been doing the interiors on the cars from Clarity Houston that have been on here recently. The tips depend upon the vehicle. Ill do my best to sum up what ive found works best in general. Wont be limiting this to 3, sorry.
1. Just like during a wash, clean from the top down (i also tend to finish the rear and move immediately to the front of the dash) This way you avoid sitting, rubbing, or greasing up areas you've already cleaned.
2. blow compressed air on all panels that are above seat level, massage contaminants out of all seams in seats and between panels, and then vacuum EVERY square inch (not including the carpet/floor). Otherwise youre just grinding dirt into those areas. Leave floors for when youre absolutetly 100% done moving around that part of the car.
3. clean areas in the order of what product youre using; keep your glass for last to avoid streaks. Dont clean your windows and go dress the panels next to them, you'll have a nice greasy border.
4. leave your seats and floors for absolute last in their respective sections. I have the entire rear of the car clean before i touch the seats because they are inevitably used during detailing. My drivers and passenger seats are the absolute last thing to get detailed (excluding the door cards).
5. if you arent happy with an area dont go moving on. odds are if you were to go back and go deeper into cleaning the dirt and grime there will find its way to already clean areas.
6. dont underestimate the power of steaming!
7. q-tips and other confined space tools are invaluable; your finger nail is often not deep enough for gaps between panels and door seals etc. find a tool that lets you reach these places; theyre what separates a good interior from one that looks new.