For successful use of cloth nappies you require:

Cotton Nappies
Waterproof Covers
Disposable Liners
Bottom Wiping Cloths
A Nappy Bucket with a Fitted Lid

Cotton Nappies

It helps to have nappies that fit your cover.  Too big is a hassle, and too small slips around and creates leaks.  However, nappies can be used in more than one cover size, and smaller nappies can be used as 'boosters' to increase absorbency, particularly at night.

Covers

Covers can be wiped and re-used at change time, and only washed every 3-4 changes, or when soiled.  Having covers that fit ensure a minimum of problems with leaks.

Covers are made by prorap and constructed from PUL (polyester urethane laminate) that is waterproof and breathable.
They have double leg guards to protect from explosions and come in a range of sizes - if the cover doesn't fit - then it might leak!
The covers are sized according to weight - but the fitting around the thigh is important.  A chunkier, lighter baby may be in a different sized cover to an older baby of the same weight, that is long and slim.

If you are squeezing your baby into a slightly-too-small cover - pulling the tabs firmly across a chubby tummy, then do be aware that the extra stress on the tabs will eventually cause the waterproofing to split along the 'stretchmarks' on the tabs.  Splits will mean that the waterproofing is not as effective along those lines.

If you buy the wrong size for your baby, you are welcome to exchange it (un-used and unwashed) for a larger size.

 
Disposable Liners

Liners can be washed and re-used if not soiled.  If poo-ey, they are safe to flush.

Bottom Wiping Cloths

If you are using cloth nappies, then using cloth wipes is easier than having disposable wipes, as well as avoiding nasty rashes from reactions with highly perfumed wipes. 
Use any cloth (muslin wipes, flannels, etc) and just water is fine. 
Rinse as required, and pop into your nappy bucket. 
Of course, we recommend terry towelling (which sticks to poo really well!) and the locally made CHEEKY WIPES are just perfect!

A Nappy Bucket with a Fitted Lid

Any bucket with a fitted lid will suffice.  You don't need to soak your nappies, but if you do have water in it - your bucket will need to be toddler proof in the months to come.  You can store your soaking bucket in the bath tub to keep it well out of the way of adventurous children if required.  Some parents choose to use two smaller buckets, one for the laundry, and one for by the change table.

Thoughts to Consider

 NAPPIES

The number of nappies that you require depends on your washing plans.  If you plan to wash daily, and have drying options available if the weather is wet, you will need less nappies than if you choose to wash every 2-3 days.
As your child gets bigger, the number of changes per day you can expect decreases (and so should the incidence of soiled changes!!) refer to table above for average numbers.  Therefore you will require less bigger nappies, or be able to wash less often.
The sizes of nappy you require also depends a bit on how you want to manage.  For instance, infant nappies fit into newborn covers, but they are a bit of a squeeze, and can make nappy changing a hassle at a time when you are usually tired.  Premature nappy size fit much better.
Larger nappies are more absorbent than smaller (more fabric), so it might be worth investing in the larger size if you are having trouble with leaks/frequent wetting with a smaller nappy.  A snug fit inside your nappy cover will prevent leaks, or stop the nappy sliding around inside the cover and getting dirty when soiled.
Smaller nappies can be used as a booster, if two of a larger size are too bulky.  You may need to 'double nappy' overnight when baby is sleeping through, or during the day for heavy wetting babies. You could also add a microfibre booster underneath the cotton nappy

COVERS

The number of covers you require also depends of washing, but more so on how many soiled changes you have per day, as covers often require changing only with a soiling.  Unless poo-ey, covers can be wiped, or rinsed and dried quickly.  If I'm not going to do a nappy wash, but getting low on covers, I may pull our my soaked covers, rinse and drip dry in the laundry.
When your baby starts sleeping through, you might find that the next size cover up from the one s/he wears during the day fits better with double nappies inside.  (I have found my baby has had no problems sleeping overnight (12-15 hours) in cloth double nappies).
If you aren't requiring a night-time nappy cover of the same size, then 4 covers seems to be sufficient in most situations.

LINERS

Ecobots liners cope with soaking and washing several times.
You can rinse and re-use soiled liners, but they are designed to be able to flush to minimize having to deal with too much poo.
If you are using a water resistance cream, or nappy barrier cream, such as tui bee balme - then you need to use a flushable liner to protect the nappy from becoming waterproof!