People deal with contracts every day, many times without even knowing it. Just about every transaction you enter into; at the store, at school, related to your household (mortgage, insurance), involves a contract. The best way to describe a contract is an agreement between (at least) two parties. The main issues with contract are 1. Whether you have one, and 2. What type of contract it is. A contract is formed between parties when there is an offer to enter into a deal, an acceptance by the other side, and consideration (an exchange) between the parties. If there is no consideration, there is no contract. For instance, If Person A says he will give Person B 5 dollars, and Person B says “ok,” without giving anything in return, there is no contract. This is a revocable gift. If Person B is giving something in return, then there is a deal. The consideration (the exchange) can be a thing (say, a trumpet), doing something (cutting the grass), or forbearing from doing something one has a right to do. You can also make an agreement that buys your opportunity to perform later, like a lease with an option to buy. Your lease payment buys both the use of the premises for a time, and gives you first opportunity to enter into another contract to buy the premises. The payment is the consideration, or the exchange, for the use and the purchase opportunity.
Many contracts are express, meaning you can find the agreement in the words. Contracts can also be implied, where conduct is required and you cannot find the agreement just from the words.
Also, aside from regular contracts, agreements can be found from conduct of the parties, or to otherwise insure fairness. A Quasi Contract results if a party has conferred a benefit on another party, the party conferring the benefit reasonably expects payment, and the benefited party would be unjustly enriched if the party conferring the benefit is not paid.