Everything you need to get started .......

Nappies :  Between 15 and 25 depending on the type of nappy and laundry facilities (see choosing nappies )
Wraps :  Around 4 or 5 in each size (not required for pocket nappies or all in ones).
Liners :  Bio-degradable liners (flush down the toilet with solids) or fleece, silk, polyester liners (to provide a stay dry barrier, especially useful at nightime).  Not required for a pocket nappy system.
Boosters :  For extra absorbency at night and as your baby grows. 
Bucket:   A large bucket with a tight fitting lid, for keeping your soiled nappies in
Nappi Nippas:   The nappy pin for the 21st century - an ingenious 3 way stretchy 'gripper', required for Nippa fastening nappies only.

And some useful extras to make life easier.

Nappy mesh:    Goes inside the bucket to make transferring to the washing machine easier.  Opend the drawstring before dumping the whole lot in the machine and the nappies will come out as they wash.
Washable wipes:   Flannelette or terry squares, a gentle alternative to using disposable wipes, which can be washed along with your nappies.
Wet nappy bag:   For nappy changes when you are out and about.