Sarah's got the right of it.
Before pounding them out, brine the breasts for an hour in the refrigerator in a quart of water mixed with 1/2 cup vinegar, 1/4 cup salt and 3 tbs sugar. This will keep them moist when you saute them; in turn this gives you a little extra leeway and allows you to get a good surface without drying the meat out. Make sure you don't leave them in the brine for less than half an hour or more than two. Also make sure you dry them very thoroughly before moving on to the next steps.
Place them on your board, and open them up horizontally (butterfly) with your chef's knife if you're knife is sharp enough, and you know how. Then pound out gently. Season appropriately with salt and pepper. Go very easy on the garlic. Hold off on the oregano until the chicken is in the pan, then crumble the oregano very sparingly on the chicken.
Preheat your pan to saute heat (medium high flame), and add a little oil (if you have it) and some butter OFF THE FLAME. Swirl the butter in the pan immediately to keep it from browning. You want the level of oil and butter to be less than 1/4". That is, there should be more than enough to coat the bottom of the pan, but not a lot more.
Return the pan to the flame and add the chicken when the foam subsides.
Use as much heat as you can (without burning the butter). Thin proteins should be cooked hot to get some color on the surface. The coloring comes from a chemical change (the dreaded Maillard reaction) and means a sweeter taste as well as a better texture.
When you get the breasts in the pan, give them about forty seconds to start searing, crumble a little oregano over them, then start agitating the pan now and then. The meat will stick to the pan while the sear forms, then release as a result of your shaking. As soon as it releases, it's ready to turn. Cook the second side the same way. You're looking at about five minutes in the pan, total.
(I'd adjust the heat and the time so that the butter used for cooking was pretty well browned when I was done -- but hitting this right takes a lot of experience and timing. I'm hesitant to recommend it if you don't know what you're doing going in.)
Some pantry options:
If you have any cooking oil, saute the chicken in about half oil, half butter.
If you have wine or stock, deglaze the pan with either or both, reduce the deglaze and finish with a little butter. Don't forget to pour off the cooking oil/butter first.
If you have lemon, finish the chicken with a squeeze. This is very simple and will make a huge difference.
If you have flour or breading, milk and/or egg, prepare a Milanese or you may simply bread them in flour (and omit the oregano if you do). Cook at a lower temperature you want the crust to have time to brown.
If you have flour, just lightly dusting the seasoned breasts with flour before you saute, then making a thickened butter/jus sauce with the flour left in the pan is a wonderful thing. It's called meuniere in French, and most likely, along with a splash of wine and a citrus squeeze, is how I'd do it.