Most treks will include a homestay with a local Hmong family. I recommend doing a trek and homestay with a local woman (as opposed to a guided tour). Prices range from $15-20 per night.
Treks will typically take place over three days. The first trek will be from Sapa to the homestay, around 8 kilometers, or 5 hours. The second trek will be to a waterfall the following day, around 3 hours. The third day trek is optional, and will be back to Sapa, around 8 kilometers away.
I did this trek, unguided, for under $20 USD per day. Accommodation will set you back $1-2 per night. Food will be your biggest expense on this trek, with meals costing anywhere from $4-8 USD. The higher you get in altitude, the more expensive meals will become.
This trek will take anywhere from 16-23 days.