Here is an example of what might happen in a LETS. No money changes hands for most of the trades (although Eddie will probably need to buy some cloth), but there is no direct barter, either. The LETS acts as the 'middleman', introducing trading partners and providing the local currency.
Arthur gets his tomato plants from Eddie, who commissions Denise to make a dress. Denise gets the dress designed by Fiona, who mends Beattie's computer. Beattie gives Charles an aromatherapy massage, and Charles makes a cake for Denise using eggs he gets from Arthur. Arthur also supplies his eggs to Fiona, who uses them and some tomatoes from Eddie to make a lovely omelette and tomato salad for her supper. Phew!