Part I: Adam Smith's Labour Theory of Value
This version proposes that exchange value, clearly not linked to use value, (diamonds and water paradox) must depend on something common to all commodities, and this must be labour. The example he uses is that in a primitive pre-capitalist market, it would take the same time to catch two deer as it would one beaver; therefore, the relative price of 2 deer would be that of 1 beaver. If someone take 5 hours hunting 2 deer, then they'd be willing to exchange them for a beaver that it took someone else 5 hours to hunt.
That's the basic idea, at it's core. Smith did know that society was becoming mechanised however and expanded the theory. If woolen clothing is being produced by looms, the woolen clothing will use labour in 2 ways; firstly, the labour that someone made the loom with, secondly, the labour involved in using the loom. The first is indirect labour, the second direct labour.
So, if the loom works twice as fast as making wooly jumpers by hand, the guy with the loom can afford to charge cheaper; in 8 hours work if he produces 4 items, he would make the some money by charging half the price of the guy without the loom who makes 2 items in 8 hours work.
He also recognised that if a value of a good could not be increased by labour, it must be compensated by some other common quality, such as scarcity. Monopoly is another exception, as there is no competition so goods can be kept scarce.
The general idea is, you pay for what you don't want to spend time doing. An example that Marx gives is you pay maybe twice as much for a coat than for the cloth required to make it; the idea being that the price is determined by how much someone is willing to pay for someone else to do the work. You could make the coat yourself, but you're more willing to spend (whatever) on it.
In more complex commodities this applies, but we have to consider indirect labour too, but that gets a little more complicated so I'll talk about that if we get a debate going.
Part II: David Ricardo's Labour Theory of Value
Ricardo raised an objection to Adam Smith's Labour Theory of Value to do with rent, land, and labour. Land rent appears to be a cost of production (the market price of an agricultural product depends on the rent of land) but labour is more productive on more fertile land, so crops growing on more fertile land use less labour-but don't have less value.
Ricardo concluded that land rent is enough to cancel out the differences in labour cost, (so fertility doesn't effect value) because he discovered rent is based on differential productivity.
E.g. A farmer can rent 2 pieces of land with different productivity. The more fertile field has output for 1,100 labour days and the less fertile field has output to last 1,000 labour days. So the farmer is willing to pay (roughly, unless he does his sums) an extra 10%, knowing he'll get more out of this land yes? And the landowner, knowing this land was more fertile, would charge about 10% more, yes?
So, the difference in rent is the same as the difference in productivity.
However, imagine a third field so poor that it's not worth any rent, and let's call it "marginal land." It produces 800 labour days output, so the cost of cultivation is so high it means there's nothing left for rent. So, the more fertile field has 300 more labour days of output; 300 more than zero, so on that field there's 300 labour days of rent. And the other less fertile field gets 200 labour days of rent, therefore the higher price for rent balances out the higher productivity.
So, it is the labour required for production on marginal land that determines the normal value/price of agricultural products.
While Ricardo dealt with this important criticism of the labour theory of value, he also developed a theory of rent still considered correct today, where surplus of production is absorbed by rent. This was an influence on proto-socialists, as it revealed that the landlord doesn't do anything to earn the rent, he just gets it automatically as a consequence of the competition market system.
Part III: Karl Marx's Labour Theory of Value
Karl Marx expanded on the theory in a couple of ways:
Socially necassary labour
This straightened out some minor confusions about the theory; suppose there is a clumsy carpenter who makes houses in half the time as a skilled carpenter, why aren't his houses worth more? Because the time he wastes isn't "socially necassary" labour time.
With technical progress goods are produced with less labour; are they worth less? To a degree they are, (a computer is certainly worth less than it was in the 1940s) but advanced technology also reduces the socially necassary labour time.
Essentially, value depends on circumstances and is not fixed.
Surplus Value
Ricardo's analysis of the landlords as taking away the farmer's surplus when they work on land which produces more than it costs in cultivation explains the basis of class relations in feudal times. This is why the labour theory of value is so relentlessly attacked by the establishment; it asks where the money earned by the wealthy and idle comes from.
Marx had the following insights:
1-In a competitive capitalist economy, commodities are priced at their values
2-In a competitive capitalist economy, labour is a commodity.
3-Therefore, labour is priced at it's value.
So; the wage paid for a labour day would be the labour time socially necassary to produce the labour day; that is, to ensure income is higher than expenditure. If this is done in half the time of the labour day, then the workers will get half the income of that day between them; the employer has no reason to pay them any more of the income, so he keeps the surplus to himself.
So, each day of work produces a labour-day of value, but costs less than a labour-day of value so there is a surplus-value left over. As labour produces all value, but doesn't get all value back, Marx concluded that surplus value is exploitation.
If that's too difficult to understand, think of it like this; an employer isn't going to hire someone who costs as much as he makes for the company!