Negotiating a contract can take place verbally, or in writing -- there are advantages and disadvantages of each strategy. 

Almost always, the (prospective) buyer makes the first move in negotiations -- I suggest that it takes place in written form.  A buyer can certainly make a verbal offer on a property, but putting the offer in writing has several benefits:

• All of the details of the offer (price, financing terms, closing time line, etc) can be clearly explained in a written offer.  Some details are often omitted in a verbal offer, which can lead to friction or negotiation failure later in the process.
• Taking the time to put an offer in writing demonstrates a level  of seriousness to a seller, which can add negotiating strength for a buyer.

The only advantages of making a verbal offer are the potential for faster feedback from the seller after deciding to make an offer, and the lack of commitment --- a verbal offer is not legally enforceable.

When it comes to further negotiating the terms of a contract -- after the offer has been made -- oftentimes it can be more helpful to do so verbally.  A few things to consider:

• PRO-VERBAL:  Especially if the buyer and seller go back and forth several times on price (or other terms), negotiating verbally can help immensely by speeding up the process.  If each party is making their counteroffer in writing, it can take days, instead of hours, to come to a conclusion.
• PRO-WRITTEN:  Since a verbal agreement is not legally enforceable, even if the buyer and seller agree on terms, either party can revoke their agreement at any time prior to when the agreement has been signed by all all parties.

Beyond the generalities above, either verbal or written offers or negotiations can be appropriate in a given situation.  As with almost everything in real estate --- the context is the key!