Acceptance of it, assuming the party(ies) is/are of sound mind and not under duress and assuming the contract isn't grossly unreasonable.

Your signature. It implies that you've read, understand and agree to the terms of the contract.

the agreement or a signature

Offer, acceptance and consideration.

Sadly, contracts are a passion of mine. But, in short, lots of things--it depends on the type of contract. The basic elements of a old-fashioned contract generally are offer, acceptance, and consideration. Consideration is a term that basically means you have to give up something to get something, kinduva quid pro quo. You can't contract to paint somebody's house for absolutely nothing in return (no money, no bartering, etc). This is slighly oversimplified. There are other things that need to be considered--was the person signing of sound mind, old enough, etc. A contract to do something illegal or force someone to do something against public policy (like an arranged marriage) is not binding. Some types of contracts require a date. You don't always have to "sign" a contract to make it binding. First, only the person that you are trying to enforce the contract against has to sign it. Certain construction contracts in California have to have certain language to make them valid. A lot of things makes a contract invalid and therefore unenforceable. Fraudulent misrepresentations that form the basis of the agreement. The examples are endless. If you want to give me more info in a comment I can try to tell you if it's enforceable. I answered a slightly different question than you asked, but I thought this info would be helpful. Cheers.

your signiture,their signiture and those of two witnesses

Offer, acceptance by both parties and some consideration (money or something of value). Did not sign under duress and have a couple witnesses would be helpful. Check out the legal department or contact a lawyer.