Somewhere around here, Ediese has a fabulous thread with A-Z tips on how to care for your hair while in a sew-in. It's the first regimen I used when I first joined. I'm sure you'll be able to locate it with a search.
To answer your questions:
How exactly do you get your scalp clean with a sew-in? Ediese suggested diluting your shampoo (and conditioner) with water and using a spray bottle. Spray the diluted poo or conditioner directly to your scalp and braids, and gently clean and rinse. Same concept with DC'ing- dilute it and spray directly on your braids/hair. I DC'd under a plastic cap and scarf while working out. I shampoo'd, conditioned and DC'd once/week.
And how long do you keep the weave in? I kept mine in for 6 weeks. In the Ediese's thread, she suggested not keeping it in for longer than 12 weeks. Personally, I think 10 weeks, with proper care, should be the max.
Remember to also moisturize and seal your braids/hair regularly while you're in the weave. And oh- if your weave hair starts to get too shiny from the moisturizing and sealing, a little powder combed through the weave hair will cure that.
I got 1.5" of growth during the 6 weeks I was in the weave. Good luck!