Let me know if you still need help with your question. I am a licensed Real Estate agent and a member of the Fl Bar Assoc. & Il Bar Assoc. I'm not attempting to solicit you, only trying to help. Your question...is a little vague so in order to answer it would take a little explanation.

Mike,
Yes, these two prior answers are great info. In Illinois there is an 11 page contract which is filled out by the buyer when making an offer on a home. There are several aspects of the contract that can be negotiated including price, dates, fixtures in the home, contingencies, etc. The counter offer comes into play when the seller does not agree to all of the terms of the buyers offer. Typically negotiations will go back and forth in person, via fax, or verbally. Those signatures are needed to make the contract ultimately in force however. Hope this helps!! Good luck.

Ken has provided a very good general explanation. Precise methods for transactions will vary according to state, and even by region with a given state. For example, in some areas, all counter offers are delivered in written form only, while in other areas, counter offers may be communicated verbally following an inital written offer.

Either party may put a time limit on an offer/counter for the length of time the offer will stand. If the contract is not binding upon signature, a time limit is less effective. For example, if there is a provision for an attorney to review the contract before it becomes binding, as exists in some states, the time limit becomes less effective, but might still be ulitlized.

Counter offers can be exchanged several times between the parties before such time that there is a meeting of the minds, or the parties agree to part ways.

Hello Mike,

Although I'm not in your area, I will give you a short explanation. I'm sure my fellow Trulia Agents will fill in with much broader explanations. Offers and counter offers are the negotiation process of the home. An offer is submitted by a Buyer highlighting the their terms they are willing to adhere to for purchasing the home, including price, financing and inspections to name a few. The offer is conveyed to the Seller at which time the Seller can accept and agree with the Buyers terms or send a counter offer. The Counter Offer basically will says I have reviewed your offer, however, I want the following changes made to the contract. Typical Counter Offer is a price change, change in amount of closing costs, change of closing date, and or a change of title company. Once a Buyer receives a Counter Offer, they can also counter the counter offer. The Buyer now has the ability to say "I don't agree with your terms," and establishes new terms. Once the negotiations have ceased, you either have a signed deal agreed to by all parties or both parties have decided not continue with the transaction. This has been a very very brief overview, you have rights in the process so please feel free to speak with a Licensed Realtor, they will able to walk you through the whole process.
Good Luck, http://www.C21Infinity.com