There have been may types of money and many ways of creating it. It is important to bear in mind that money is defined by its function, not its form. Money is not gold, nor debt, nor the government. Money is what money does.
What does it do? Money serves as a symmetry breaker. A barter transaction has symmetry in time, place, value, and participants. This is very limiting and a modern economy could not function under these constraints.
Money allows you so sell something to one person and then buy something from someone else at a different time and place. You can sell your labor to your employer and then use money to buy food-- you needn't work for a farmer to eat, nor for a doctor to get medical care.
Money has no intrinsic value--a thing is worth only what someone will give you for it. If you were marooned on a desert island with a million dollars, it would be of no use since there would be nobody willing or able to give you anything for it.
Money can make an individual rich, but it cannot make a nation rich. The wealth of a nation depends on its capacity to produce things people want. Mercantilism is an economic dogma resulting from belief in the illusion that money has value. Mercantilist nations compete to accumulate more gold, money, or whatnot, but those things cannot make a nation rich. Only real productive capacity can do that.
The important attributes of money are its supply, demand, and price. These are simple concepts but the devil is really in the details here.
Nobody knows exactly how much money is in circulation at any one time. There are ways to estimate it, but a discussion would require a long digression. Money takes more than one form: cash, bank deposits, etc., and there are disagreements about what to count. The balance in your checking account certainly counts, even though it is nothing but magnetic spots on some bank's disk drive, but what about a savings account? A Treasury Bill? A bag of silver coins in a safe? In general, liquid assets you intend to spend are money. Illiquid assets you don't plan to spend for a while are not, but can be converted to money when the time is right.
In a modern economy money is created by a central bank. In the US, that means the Federal Reserve. Central banks have the authority to print money. They spend it to put it in circulation. What they usually spend it on are government bonds, but sometimes they buy foreign currency and they may buy other assets should the need arise. When the central bankers want to increase the money supply they buy assets. When they want to decrease the money supply they do the reverse--they sell some of their assets and take the seller's cash out of circulation. These are called "open market operations" in the US, and other nations have analogous procedures.
Another way money is created is by lending. Imagine all the banks in the nation glommed together into one big bank. You go to the bank and deposit your money. Contrary to popular belief, the bank does not hold your money for safekeeping. You give it to them and they give you a receipt that says you can exchange that receipt for a certain amount of money at a future date. You are a lender to the bank. The bank takes your money and lends it to somebody else, who spends it on a new car or whatnot. The seller of the item now takes the money and puts it back in the bank. Your money is still in the bank, and now the seller's is too--the bank has xeroxed your money! Economics texts use terms like "balance sheet expansion" or "deposit creation" for this process. The process can go on and on forever, creating an infinite amount of money--until somebody defaults on a loan. When that happens the whole thing unwinds and comes crashing down like a house of cards. For this reason banks are regulated by the government. In the US the Federal Reserve plays a major role, but other agencies are also involved. The xerox machine must not be allowed to get out of hand or the financial system could become dangerously unstable. Banks are required to keep some of their capital in reserve to absorb losses, and the central bank requires that they deposit a certain percentage of their assets with them where they cannot be loaned out and earn no interest. This money is called "Fed Funds" and the "Fed Funds Rate" is the interest rate banks charge each other to borrow these funds. The Federal Reserve controls this rate and you will often hear talk of it on TV and in the papers. They also control the amount the banks must deposit with the Fed; this is called the "reserve ratio." In addition to regulating bank's lending, central banks serve as pawnshops for commercial banks. Since most depositor's money has been lent out, there can be problems if many depositors want to withdraw their money at the same time--because it isn't there! If the bank is solvent it will have the assets necessary to pay all the depositors, but not in the form of cash. The assets will be in the form of IOUs from borrowers which have value but are not suitable for paying off depositors. When this happens it is called a "liquidity crisis," and in such situations banks may take their IOUs to the central bank and pawn them for cash to pay off depositors and avoid a run on the bank. The central bank buys the IOUs at a discount, and the amount of the discount determines the cost to the bank of this service and is equivalent to an interest rate on a loan using the IOUs as collateral. This rate is called the "discount rate" and the facility for such borrowings is called the "discount window." The central bank controls the discount rate. In normal times banks prefer not to use this facility since it might imply they are in financial difficulties but the central bank can encourage its use by setting the rate lower than market rates. In a crisis it can be an important means of keeping the banking system lubricated.
The demand for money isn't what most people think it is. Isn't it infinite? Doesn't everybody want as much as they can get? Not exactly. Imagine you won the lottery and got a million dollars cash. What would you do? You would spend some of it, invest some more, and keep some of it in your wallet and your checking account. Your demand for money is how much of it you want to keep in cash--not what you spent or invested. It's your demand for short term liquid assets, not your desire to be richer. It's impossible to know exactly what the demand for money is, though it can be estimated. In general, the demand for money rises as you become richer, or if prices are stable or falling, or if there are few attractive alternatives for parking your wealth.
We don't know the supply of money, or the demand, but at least we know its price! If an ounce of gold costs $600, then the price of a dollar is 1/600th of an ounce of gold. If 100 Yen cost a dollar, then the price of a dollar is 100 Yen. When the value of money is increasing, we have deflation. When the value of money is decreasing, we have inflation.
The price of money is arbitrary. If another zero was added or subtracted from everybody's bank account, nothing would change. Prices and wages would immediately compensate and credit contracts would compensate for the change also--if the change was known in advance. If the change came as a surprise, a massive income transfer would occur between parties who had agreements to transfer funds in the future.
It's tempting to think that inflation and deflation don't matter if everyone sees it coming. Not quite. They have different effects on people's willingness to hold cash. In inflationary times, cash becomes a hot potato--a wasting asset to be spent or invested quickly. In deflationary times, cash gets more and more valuable the longer you hold it--you would demand a premium over the deflation rate to be induced to invest. Suppose prices are falling 3% per year and you have a million bucks stuffed in the mattress. You make 3% doing nothing, so naturally you won't loan out those funds unless someone offers you a better deal. Suppose a borrower offers to pay you 1% on your money. Because prices are falling (i.e., the price of money is increasing), the dollars you are repaid have a purchasing power 3% more per year than those you lent. Even though your nominal rate is 1%, your real rate is 4%--borrowers must scrape up 4% per year more purchasing power than they borrowed, even though the nominal value of the cash is only 1% more than they borrowed. Moral of the story: deflation tends to make credit less available and more expensive than stable or rising prices. If the deflation is severe, credit may dry up and investment will virtually cease. This can destroy an economy since lack of investment will hurt productivity, and in the long run productivity is the only determinant of a nation's standard of living. Inflation is a somewhat different story. If inflation is running at 3%, you would be anxious to lend your money out because if you sat on idle cash it would slowly disappear. In this case a nominal rate of 1% yields a negative 2% real rate. If a lender wants to receive the same 4% real return as in the deflationary case, a 7% nominal rate would be required. Even though the interest rate is much higher, borrowers would be willing to pay it because they would be repaying their loan with dollars that were "cheaper" than the ones they borrowed. Moral of the story: inflation, if known in advance, tends to make credit available by penalizing holders of idle cash, and the interest rate can compensate for the change in prices. If the inflation rate comes as a surprise, income transfers between lenders and borrowers will occur.
If prices are 1/10th or 10 times what they are today, it makes no difference, but getting from "here" to "there" can be a rocky road indeed!