A bubble wand is a long, porous stick that, when air is forced into it, it lets it leak out in tiny bubbles all along the stick. A bubble stone is simply porous material in a small (medium or large) chunk that you can place in your tank. There are also bubble "disks" that are porous material in a circle formation that make a column of bubbles.
These are attached to an air pump by way of plastic tubing. Tubing can be blue silicon, clear plastic or even black plastic (stealth) so that it is not easily seen in a tank. AS mentioned above, there are things called "Check valves" that need to be used. The tubing is held in place in a tank - running down the back walls or wherever by small suction cups that have clips for the tubing.
So - depending on how deep your tank is, how long or big the air feature is, etc, you will need an air pump that is capable of pushing a large enough amount of air that it can force the air out the pores of the air feature. On the boxes of various pumps, they usually list the number or length of air features. I tend to like to go BIG on an air pump and then turn it down so I can control exactly how many bubbles I get.
SEt the air pump up next to the tank. Cut a small piece of tubing - about 3 inches long and attach it to the air pump. Next, you want to add something called a "Check Valve". This is a little valve that allows air to go one one through it, but will not allow water to come back the other way. If, for some reason the air pump stopped pushing air through the tubing, you do not want water to syphon back through the airline hosing into your air pump and ruining it. Check valves are cheap. To this, if you have a large enough pump, I attach another length of hoseing that leads to the top of the tank. I like having air control valves to regulate the amount of air to the various features. These can be large ganged metal contraptions or simply plastic rotary valves - look around in the stores at the airline tubing aisle. You will find all kinds. They all work well - it is a mtter of what you like. On the other side of the valve, you will then attach more airline hoseing that will lead to the bottom of the tank and the air feature. Small suction cups can hold the tubing to the interior sides of the tank to keep it out of the way and out of sight. If you have gravel, you can bury the hosing under the gravel as it goes to the air feature.
I also like recommending a "drip line" on this - meaning that as you follow the airline tubing out of the tank, it will go out, drop down in a loop that is LOWER than the air pump and then back up again to where it attaches to the check valve. This is another saftey feature. If any water were to run along the hosing, it will run to the lowest point and drip off - the lowest point being someplace OTHER than your air pump. Again - a protection from electrical shorts and such.
If you get a big enough pump you can run many features off them. The larger the feature the more air it will need. The deeper the tank, the more pump you will need.
Have fun. It is a ton of fun to add a bubble column and watch the goldies riding it like a carnival ride - up and down, waiting in line to go up again!