Change those big bills for small ones. Nothing kills a deal like settling on 10 pesos and handing over a 100 peso bill. Small change is also useful to cover purchasing little trinkets as well as a bottle of water to keep your energy going. Carry your money in a small change purse close to your body and try not to count money in front of vendors.
Practice some basic Spanish niceties and phrases. Greet vendors with, "Buenos dias," or "Buenas tardes." To ask about a price, say, "Cuanto cuesta," or "Cuanto vale?" End with, "Gracias!"
Keep a poker face. When the vendor announces the price, don't recoil in shock or jump for joy. Continue to inspect the item in question. Pick up some other items to compare. Never dismiss the item or insult the wares, but rather express a friendly yet detached interest. Always be prepared to walk away.
Step back or look around, keeping a friendly expression. The vendor may jump in and offer a discount at this point. If not, ask in a friendly way, "Hay discuento?" or "Is there a discount?" Another option is to ask if it's her best price: "Es el precio mejor?" You can also ask for a discount if you plan to make a large purchase.
Maintain the positivity of the exchange. If the vendor refuses to bargain, you can walk away. Or you can say you will return later, after looking around. If you must have that treasured item right now, try asking more friendly questions about it. Ask who made it or where it's from. Ask if there are other colors or different sizes. By showing more interest, the vendor may warm up to the situation and offer a discount.
Thank the vendor. Whether you wound up with the item or just had a quick Mexican adventure in bargaining, you have gained something from the transaction. There are always more items and more vendors so relax and enjoy yourself.