The Basics
All coins are silver or gold, including the pennies. If someone gives you a modern copper penny, tell him it is too debased to use.
frequent missapplication: There is no copper money. Some older coins are debased with copper or brass, but no one would mistake a shilling for a penny on this basis. There is no paper money. You cannot, for example, have a 5-pound note. The basic denominations are pounds, shillings, and pence.

12 pence make a shilling
20 shillings make a pound

In writing, the abbreviation for:

penny is d
shilling is s
pound is £

The Coins In Your Pocket
A sovereign is a gold coin worth 1 pound (but try to think of it as 20 shillings).
There is no coin called a "pound" until after 1583, although that is the basic monetary unit. The angel is one of the most common gold coins in circulation. The angel is worth 10 shillings (1/2 pound).
You would never say you owed somebody 6 angels. But you might say you gave your servant an angel to spend at the faire. To coerce someone's servant, you might suggest that the sweet voice of an angel would convince him.
The crown is the most common coin, worth 5 shillings, issued in both gold and silver. The crown is also equal to a Venetian ducat, a Flemish gelder, or a French êcu (sometimes called a French crown).
Half-a-crown is worth 2 shillings 6 pence (sometimes expressed as "2 and 6").
The shilling is a silver coin worth 12d.
The sixpence is a silver coin worth six pence.
A groat is a silver coin worth 4 pence.
The penny is a silver coin worth a penny (never a pence).
A coin worth 2 pence is called tuppence.
A half-penny is called a ha'-penny (not a ha'pence).
The farthing is a 1/4-penny fragment so tiny as to be impractical, but still in circulation from less inflated times.
The guinea does not yet exist, and will not be minted till the late 17th century. Don't refer to it.
The mark is "money of account". That is, it is a value worth 2/3 of a pound (13s 4d) but there is no coin worth that amount in the 16th century. It is often used in high-level transactions, such as selling land, figuring feudal fines, or calculating dowries.

Spending
In practice, people seldom speak of ordinary amounts of money in terms of pounds,
unless it was in thousands, like the annual value of an estate, or a special "voluntary" tax. You probably think of ordinary, daily expenses in terms of shillings and pence. ("I lost 7 crowns last night at tables.") Money bought more in those days. Do not just substitute pounds for dollars. Try using shillings, or even pennies, depending on the item. Twenty pounds for a pair of gloves is highway robbery. But 20 shillings for a pair of gloves doesn't sound so bad, at least theatrically speaking. (Actually 7 shillings is closer to the truth.) For smaller items, like food and drink, use pennies. A penny or two for a beer is about right, where 2 pounds or even 2 shillings is unthinkable. Tip a household-type servant no more than a few pence. Remember, he only makes £2-5 per year! (Note: that tip is called a vail.) A common vail is about 3/4d. If you're buying information or a favor from anybody besides a servant use gifts instead of money. For servants--use money!