Adam Smith, the father of modern economics, sought to demonstrate that markets (and economies) pre-existed the state, and hence should be free of government regulation. He argued (against conventional wisdom) that money was not the creation of governments. Markets emerged, in his view, out of the division of labour, by which individuals began to specialize in specific crafts and hence had to depend on others for subsistence goods. These goods were first exchanged by barter. Specialization depended on trade, but was hindered by the "double coincidence of wants" which barter requires, i.e., for the exchange to occur, each participant must want what the other has. To complete this hypothetical history, craftsmen would stockpile one particular good, be it salt or metal, that they thought no one would refuse. This is the origin of money according to Smith. Money, as a universally desired medium of exchange, allows each half of the transaction to be separated.
Barter is a system of exchange by which goods or services are directly exchanged for other goods or services without using a medium of exchange, such as money. It is distinguishable from gift economies in that the reciprocal exchange is immediate and not delayed in time. It is usually bilateral, but may be multilateral (i.e., mediated through barter organizations) and usually exists parallel to monetary systems in most developed countries, though to a very limited extent. Barter usually replaces money as the method of exchange in times of monetary crisis, such as when the currency may be either unstable (e.g., hyperinflation or deflationary spiral) or simply unavailable for conducting commerce.
Make the deal. After you've found a barter partner, get the agreement in writing. Make sure you detail what services or goods will be involved, the date of the exchange (or work to be done) and any recourse if either party reneges on their part of the deal. If you are working through a membership-based bartering association, they will likely provide all the structure and paperwork you need for the deal.