Yes - you will be glad to hear that this is easy!!
Firstly, you need to put the Action you recorded in a new Action Set - click on the little folder icon at the bottom the the Actions palette. You have to do this as you can't save an individual Action, just Action Sets (apart from 'Droplets' - but they are not Actions as such).
Click on the name of your Actions Set in the Actions palette, then bring up the sub-menu (click on the little arrow, top right of the palette) and go down to 'Save Actions'.
It's best to save Action Sets, Brushes and all other extras in the Photoshop default location - you will then be able to load them quickly and easily on the sub menus. They are all stored in the 'presets' folder within the Photoshop Application folder on your computer.
If you are on a Mac goto HD>Applications>Photoshop>Presets>Photoshop Actions
The main thing to watch out for is steps in your action that save a file - if the Action is run on a different computer it will error out on the first image you run it on, because the file path is different. The easiest way to fix this is to re-record that single step on the computer you wish to move your Action to and resave the Action. You can also use File>Automate>Batch to run Actions which also allows you to define a new save path that will overide the one in your Action.