Trick to keeping guacamole from turning brown

The California Avocado Commission recommends this (safe but wimpy - see below for a better way) three-step process:

1. Start with a ripe avocado and cut it lengthwise around the seed. Rotate the halves to separate.
2. Remove the seed by sliding the tip of a spoon gently underneath and lifting out. The other common seed-extraction method - striking the seed with a knife and twisting - requires some skill and is not recommended.

3. Peel the fruit by placing the cut side down and removing the skin with a knife or your fingers, starting at the small end. Or simply scoop out the avocado meat with a spoon. Be sure to sprinkle all cut surfaces with lemon or lime juice or white vinegar to prevent discoloration.

   

Source: California Avocado Commission

Notes:

• Another (and my favorite) way to remove the pit is by holding the half with the pit in one hand and striking the sharp edge of the knife used in step one into the pit, then twisting to remove. This is the "pro" way to do it, but takes a little practice. The video Nate referenced in the comments shows how to do it, it's not that hard.
• If you're going to be chopping the avocado up, you slice it up using the tip of the knife still in the shell, then scoop the sliced avocado meat out with a spoon.

I am not familiar with nopales, but I would be astonished if their green color was determined by something else than chlorophyll. Chlorophyll is usually destroyed by normal cooking techniques. If you want to keep the color mostly green (some dulling is inevitable):

• cook the vegetable in an alkaline fluid. The easiest way is to use water with some baking soda added. The problem here is that humans like food which is slightly acidic, and alkaline food tastes soapy. Also, vegetable fibers soften more easily in alkaline environments, so they will be somewhat mushy. So use a very small amount. If they are to be added to a dish which is acidic (in a Mexican dish, the culprit will probably be tomatoes), cook the green vegetable separately, and only combine it with the rest of the dish at the last possible moment. Right before serving is best.

• Heat destroys chlorophyll too. Cook the green vegetable as short as possible. Blanching is perfect, don't forget the ice bath at the end. It will probably be enough as a preparation method. While I don't know how hard a nopale is, I find blanching to be quite sufficient even for broccoli (provided the water contained either salt or baking soda), and their stems are one of the woodiest things we eat. If you don't think they are softened enough after blanching, cook them longer, until you find they are sufficiently softened.