A contract (or K) is a promise enforceable at law. That means that if someone breaks their promise, you can take them to court.
Not all promises are enforceable at law. For instance, the following does not create a promise enforceable at law.
Her: Honey, does this dress make my ass look fat?
Her: You promise?
A breach of that promise (the dress does indeed make her ass look fat) is not enforceable. It is not enforceable for three reasons; 1) No consideration has been given by either party; 2) At early common law, almost all judges were men; and 3) She has no remedy except to diet (that is, you cannot make her ass look less fat in the dress).
A valid contract requires:
1- Mutual assent;
3- A Piece of Paper;
4- A Pen;
5- Two or more parties;
6- Reasonably specific terms.
The parties must be agreeing to the same thing. If one person is agreeing to buy "yellowcake" from Niger and Niger is agreeing to sell Rice Crispy Treats, there is no mutual assent.
Each party must have something of value on the line, whether time or money.
Piece of Paper, Pen and Two Parties
Most contracts should be in writing, so have paper and pens readily available. You cannot enter into a contract with yourself, so round-up another warm body if your just dying to go out contracting.
Contracts for political assassination and mob hits should never, ever be put in writing. The very suggestion is considered bad form. In these situations, never make the other party 'nervous' or 'jumpy'.
Further, illegal contracts are never enforceable, so make all you want. However, be forewarned, if you hire someone to 'off' your Contracts professor and that person does not perform, no remedy is available.
Reasonably Precise Terms
The terms of any contract must be reasonably precise. Not every detail need be memorialized but the major ones should be set forth for there to be a valid contract. Agreeing to sell the "watcha-ma-callit" for "a couple two-tree hunrid C' notes" to "what's-his-face" is probably not precise enough to be a valid agreement.*
*You may nevertheless want to go forward with the deal to avoid orthopedic surgery
The Statute of Frauds
Not all contracts need to be in writing. However, some contracts must be in writing, hence the Statute of Frauds. The Statute of Frauds requires certain contracts be reduced to writing, including;
1- Contracts for the sale of real property;
2- Fraudulent Contracts for the sale of real property the 'owner' doesn't really own.
A Wide Variety of Contracts
There are many types of contracts; quasi-contracts, contracts implied in law and contracts implied in fact. These contracts are typically found when a 'real' contract is absent but the judge is so disgusted with one of the parties that he wants to screw them over for being such assholes.
Court created contracts are my favorite type of contract because they are designed to stick-it to really cheap, sleazy bastards. Example:
A is a residential home painter who has a contract to paint B's house. A accidentally goes to C's house which needs a really bad paint job. A begins work believing that he is painting B's house. C, a real piece of shit, knows A is mistaken and doesn't say anything but only snickers. C allows A to paint his house and then denies him fair compensation. A is distressed because he doesn't know the other letters in C's name and believes he's out of luck.
In that example, the Court will tell C to pay up and to reveal the other letters in his name. There was no true contract but the court will apply equitable principles because C is a scum-bag.
That's about all you need to know about contracts for now.