before cleaning carpets, first of all I always dust and vacuum the dash-board, console, vents, gear stick, hand brake, seats and so on all areas above the carpets, I have seen so many car valeters vacuum the carpets then clean all the dash vents and so on after vacuuming, am not saying that`s the wrong way to do it, but i just think you put all that effort into the vacuuming then you go and knock all the bits back onto the carpets.
I think it is much easier to do all that first then go ahead and vacuum, if there are mats I usually take them out and brush them down with a stiff brush, then vacuum them.
Then I go ahead and vacuum the carpets in the car, vacuuming all the larger debris first, then for the smaller bits in the carpets I use a stiff brush on them, brushing all to one corner and vacuuming again.
Now starting with the driver's side I spray my cleaning solution on the carpet then spray all the other carpets to let soak.
Back to the driver's side with a bucket of warm water and a clean microfiber cloth I agitate the solution into the carpets using a bit of elbow grease were dirtiest, then vacuum with my wet vac.
Repeating this on all carpets and mats, then I go over them with a clean dry microfiber cloth.
Your carpets should take an hour or so to dry off depending on the time off-year, you can always run the engine with the heaters on if you want them to dry quicker, but always leave a couple of the windows open an inch or so to stop any condensation.
your carpets should now be clean and fresh.