Depends on the knife. First thing the knife gets is a quick look over checking blade, blade play, construction, fit and finish, etc. After that I usually test the sharpness if that is bad I sharpen it otherwise it's left alone for the time being. I tend to be more lenient with a new blade than a blade I just sharpened, I like to get a feel for the fresh out of factory performance a lot of times before I put my own edge on it.
As for equipment, I got in a DMT Alinger with C/F/EF stones a little while ago so I am using that now with a leather belt as strop. Basically the Aligner is just there to re-profile after that first re-profile it's all done by hand when it comes to sharpening. As for specifics on what I do here I can't say as they are changing quite frequently as I have been practicing and changing my technique a lot in the past week or 2. A week ago I got a sharp edge on this setup, a few days latter I found a way to get an even better edge by a significant margin, than a day latter I found another way to improve by a significant margin without even using a strop. And once my "Box O Knives", aka my box of freshly purchased knives is delivered early next I probably get even better as I have a cheap dedicated kitchen knife bought to practice on so I don't feel bad about dulling my EDC's just to sharpen it back up.