First, select somebody to take the offer to the seller for you. Most people are too emotionally tied up in the sale to do a truly effective job of negotiation for themselves. Choose a realtor or a friend with a good business sense to be your "agent". (Every time I have ignored this advice I ended up paying too much or charging too little.) The added benefit of this process is that you don't have to make spot decisions and can consider a "deal" for a day or two before committing to it.
The offer should be written down. Include the following information: Date of Offer, Property Description, Owner's Name, Buyer's name, Price, Earnest Money, Method and Dates of Payment, and Date of Possession of the Property. Review the situation of property taxes and be sure you establish who is responsible for them, as well as stamp duties and legal fees. In most cases you will want to include a provision for a title search and for the method of transfer of title. In the case of "buying on time" it is advisable to register your sale agreement as a charge on the title until it is paid off and you can get your deed. Set forth all the details and sign the offer. Make the offer good for a particular period of time, so that after a week or so it "expires". You don't want to leave "open" offers laying around, as you might end up obligated to buy something after you've lost interest.
If the seller says "yes" s/he will sign your offer as written. If the Seller wants to change some provisions in your offer, there will be a "counteroffer", which should also be in writing. If you agree, you sign that counter-offer and proceed to satisfy the rest of the terms on the contract. If you haven't yet arrived at an agreement, you can keep offering and counter-offering until everybody is in agreement about the transaction.