Then we agree a day rate for that period. (I have a VAT-registered trading name through which you will be billed, saving problems with PAYE and the tax man).
We agree a minimum-maximum cost estimate. I try to keep unexpected costs to zero by calculating likely meetings, travel, etc, inclusive with the overall fee so you know precisely what you’re in for at the outset.
I always tender a fully itemised, VAT-inclusive invoice, detailing hours and days worked.