opener have just a few brands. There are Universal remotes that can be programmed to cover 90% of all "rolling code" openers. Unless it was 40 years old opener yours probably is a rolling code one.
The DIP type that relys on several switches are easily controlled by someone and were phased out long time ago.
What is the brand of your opener, BTW?
Most likely you are one of the many LiftMasters. In that case you have to find out the color of a "study button". It may not be green totally.
It could be purple, red, orange, green etc. Each needs different remote frequency and algorithm, or find a universial remote like LM375. http://www.usdoorcontrol.com/item-629.html
In most cases eBay is your best bet for lowest price and most variety.
